Gemara

94a (Beraisa - R. Eliezer ben Yakov): If one stole wheat, ground it, kneaded and baked it and separated Chalah from it, his Berachah only angers Hash-m - "a thief who blesses, blasphemes."

(Abaye): He holds that Ein Shinuy Koneh (changing a stolen object does not acquire it).

Rejection (Rava): Perhaps he holds that Shinuy Koneh. However, one may not bless because it is a Mitzvah ha'Ba'ah b'Aveirah!

96a (Rav Papa): If one stole a date tree and cut it down, even if he plants it in his property, he did not acquire it. Initially it was called a date tree, and also now! If he stole a date tree and made logs, he did not acquire them, for they are called date logs. If he stole logs and made beams, he acquired them.

(Rava): If one stole a Lulav and pulled off the leaves, he acquired it. Initially it was called a Lulav, and now it is leaves.

Sukah 29b (Mishnah): A stolen Lulav is Pasul.

Question: The Mishnah disqualifies without distinction, i.e. even after the first day when it need not be "Lachem", i.e. yours. What is the reason?

Answer #1 (R. Yochanan and R. Ami): It is a Mitzvah ha'Ba'ah b'Aveirah:

Answer #2 (Shmuel): The Mishnah discusses Yom Tov Rishon. On Yom Tov Sheni one is Yotzei with Gazul, just like he is Yotzei with borrowed Minim.

Sukah 30a - Rav Huna (to myrtle vendors): When you buy myrtle from Nochrim, do not cut them yourselves. Let the Nochrim cut them and give them to you.

This is because Stam Nochrim steal land, and land cannot be stolen (it always belongs to the original owner). If the Nochri cuts the myrtle, the owners despair takes effect in his hands, and you acquire through Shinuy Reshus.

Question: Even if the vendor would cut it, there would be despair in the vendor's hands, and Shinuy Reshus when the buyer gets it!

Answer: Rav Huna's counsel was for the myrtle that the vendor himself will use.

31a (Rav Nachman): If one stole wood and used it for Sechach (all agree that he is Yotzei, for he acquired it and) he merely owes money.

Rishonim

Rambam (Hilchos Lulav 8:1): If one of the four Minim was Gazul or Ganuv, it is Pasul, even after Yi'ush.

Rosh (9:1): If one stole wheat, ground it, baked it and separated Chalah from it, his Berachah angers Hash-m - "a thief who blesses blasphemes." Shinuy is Koneh, but one may not bless (for it is Mitzvah ha'Ba b'Aveirah).

Tosfos (Sukah 30 DH Ha) and Ran (Sukah 13b DH ul'Inyan): Mitzvah ha'Ba'ah b'Aveirah applies only if he never acquired it, or if he acquired it through doing the Mitzvah, but not if he acquired it before the Mitzvah. Bava Kama 94a suggests that even after acquiring through Shinuy, one may not bless due to Mitzvah ha'Ba'ah b'Aveirah. This is a mere Dichuy. Alternatively, we are more stringent about a Berachah.

Mordechai (Sukah 747): Riva forbids mid'Oraisa to diminish the berries of a Hadas on Yom Tov to make it Kosher. If one did so it is not Pasul due to Mitzvah ha'Ba'ah b'Aveirah. Similarly, if a Nochri made (detached or fixed) a Shofar on Yom Tov one may be Yotzei with it. If the four Minim were brought from outside the Techum for Reuven, another Yisrael may be Yotzei with it. Perhaps even Reuven may, for it is a Mitzvah. We learn from a Sukah made from stolen wood; all agree that is Kosher. Also, a stolen Lulav is Kosher on the second day. The reason one may not get Kaparah through a Vlad Temuras Asham is because it came through an Aveirah (Temurah 20b), i.e. a Yisrael transgressed "Lo Yamir."

Bigdei Yesha (3): We may offer Temurah of an Olah or Shelamim, even though it came through an Aveirah. Temurah is Pasul only for Kaparah. Why does Mitzvah ha'Ba'ah b'Aveirah disqualify Lulav, which is not for Kaparah? Since the Mitzvah of Lulav is obligatory, it is like an Asham.

Tosfos R. Peretz and Tosfos Rashba (Pesachim 35b DH Aval): Mitzvah ha'Ba'ah b'Aveirah applies only to Mitzvos like Lulav, which we use to praise Hash-m and appease Him, or Korban.

Ramban (Pesachim 35b DH Yesh): Mitzvah ha'Ba'ah b'Aveirah does not apply to an Isur like Tevel, which can be fixed. Mitzvah ha'Ba'ah b'Aveirah is only mid'Rabanan; the Gemara brought an Asmachta from Nevi'im. Some disagree, and say that mid'Oraisa, a stolen Chatas does not atone.

Poskim

Shulchan Aruch (OC 649:1): If any of the four Minim was stolen, it is Pasul, before or after Yi'ush. However, if he acquired it before the Mitzvah, e.g. he stole a Lulav and trimmed it, it is Kosher, for he acquired it through Shinuy.

Source (Gra DH Aval): One who stole wood and built a Sukah is Yotzei if he acquired it beforehand through Shinuy (31a). A Lulav of an Asherah is Pasul due to Kesusei Michtas Shi'urei, not due to Mitzvah ha'Ba'ah b'Aveirah.

Shulchan Aruch (ibid.): However, he may not bless on it.

Source (Gra DH u'Mihu): We learn from Bava Kama 94a.

Kaf ha'Chayim (12): After acquiring it he owes only money, so he is Yotzei. Nevertheless, he may not bless since he acquired it through an Aveirah.

Bi'ur Halachah (11:6 DH ul'Inyan): The Magen Avraham allows to bless when there was Yi'ush, but the Gra and Taz say that even then one may not bless.

Question: The Gemara suggested that the Yisrael can cut the myrtle himself and acquire through Shinuy ha'Shem. If acquisition through Shinuy does not allow one to bless, this is why the Nochri must cut them!

Answer #1 (Magen Avraham 2): Perhaps Shinuy ha'Shem with despair is better than Shinuy alone. This requires investigation.

Answer #2 (Maharsha Bava Kama 67a DH Omar): Indeed, we asked that in any case they are Yotzei through Shinuy ha'Shem, but they may not bless.

Answer #3 (Gra 11:22): In any case the Yisrael acquired the myrtle. The only concern was lest it was stolen and he is called a blasphemer. We are stringent only when it was definitely stolen. To be Yotzei a Mitzvah, we are concerned even for a Safek. We are not so concerned for a Berachah on something stolen, which is forbidden only due to an Asmachta.

Kaf ha'Chayim (16): One may not bless on anything stolen, even if there was Yi'ush and Shinuy Ma'aseh or Reshus, unless it is only Safek Gezeilah.

Rema (637:3): One may not cut Sechach (from a Nochri's forest) himself, for one may not make a Sukah from Gezel l'Chatchilah. Rather, he buys from the Nochri.

Mishnah Berurah (12): It is permitted also if David cuts and gives to Levi.

Mishnah Berurah (13,14): Perhaps the Nochri stole the forest. If there is no alternative, one may cut it himself with the owner's permission. Perhaps in this case one may bless Leshev ba'Sukah, for most Nochrim have their land through the government, and the law of the kingdom is binding.

Bi'ur Halachah (DH Ela): If a Nochri stole wood from government land, perhaps despair applies, for the government knows that there are thieves.

Shulchan Aruch (OC 646:2): If a myrtle branch has more berries than leaves it is Pasul. If one removed berries (to make them the minority) it is Kosher. One may not do so on Yom Tov. If one did so, or took them one by one to eat, it is Kosher.

Kaf ha'Chayim (646:17): This shows that if an Aveirah was done with a Lulav, e.g. it was brought from outside the Techum, it is Kosher. Some allow even the transgressor to use it; Mitzvah ha'Ba'ah b'Aveirah applies only to stolen items. If one did a different Aveirah, we do not tell him not to do a Mitzvah.