Gemara

(Mishnah - R. Shimon): If one stole Hekdesh from its owner's house and slaughtered, he pays four or five for Kodshim with Acharayos.

Question: R. Shimon holds that Shechitah that does not permit the meat is not called Shechitah. Shechitah of Kodshim (outside the Mikdash) forbids the meat!

Answer (Rav Dimi, citing R. Yochanan): The case is, it was unblemished, and he slaughtered it in the Mikdash Lishmah (for the sake of the owner).

Question: If so, (the owner was Yotzei.) It is as if the thief returned the animal!

Nedarim 35b (Mishnah): A Kohen may offer, for one who is Mudar Hana'ah (may not benefit) from him, bird-offerings of a Zav or Zavah or a woman who gave birth, Chata'os and Ashamos;

Question: Are Kohanim (serving in the Mikdash) Shluchim (agents) on behalf of us (Yisraelim), or on behalf of Hash-m?

Answer (Mishnah): He may offer for him bird-offerings of a Zav...

If he is the Yisrael's Shali'ach, he benefits him!

Objection: If he is Hash-m's Shali'ach, he should be able to offer all Korbanos! Rather, Mechusar Kipurim (Korbanos that complete Taharah) are different.

(R. Yochanan): Any Korban brought for Levi requires Levi's consent, except for Mechusar Kipurim, for one brings them for his minor children (even though a child has no intent).

Question: If a Kohen is a Yisrael's Shali'ach, why can he be Mefagel (disqualify a Korban through improper intent? One cannot forbid (through intent) what is not his! One makes a Shali'ach only to help him, but not to harm him!)

Answer: Pigul is an exception. It says "(ha'Makriv Oso) Lo Yechashev" - in any case (intent of the one who offered it counts, even if it is not his Korban).

Kidushin 23a (Rav Huna brei d'Rav Yehoshua): Kohanim who serve in the Mikdash are Sheluchim of Hash-m. They could not be Sheluchim of Yisrael, for one cannot appoint a Shali'ach to do something that he himself cannot do!

41b (R. Yehoshua ben Korchah): Why does it say "all of Yisrael will slaughter (the Pesach)"? Only one person slaughters (each Korban)! Rather, this teaches that we attribute a Shali'ach's actions to the one who appointed him.

Other verses teach about Shelichus for divorce and Terumah. We could not learn from Pesach, for most matters of Kodshim are done through Sheluchim.

Rishonim

Rambam (Hilchos Nedarim 6:5): A Kohen may offer Korbanos for one Mudar Hana'ah from him, because Kohanim are Hash-m's Sheluchim, not the owners'.

Or Some'ach: The Yerushalmi explains that the Kohen may offer his own Kinim, Chata'os and Ashamos for the Mudar; it is like paying his loan, which is permitted. He may not do so for Kodshim Kalim, for this is like giving a gift (the Mudar receives the meat). We permit for Kodshei Kodoshim even if there is Acharayos. Even R. Shimon says Davar ha'Gorem l'Mamon k'Mamon Dami (it is considered a person's property, since if it is lost, he must bring another) only when it is lost. When it is here, he agrees that it is Hash-m's. One cannot sell an Olah. It seems that the Madir (from whim the Mudar may not benefit) may offer his own animal for the Mudar only for Korbanos of Mechusar Kipurim, which do not require Da'as of the Miskaper (the one for whom it is offered). He may offer it even with the Mudar's Da'as, since it is not Shelichus. It is like paying his debt. Other Korbanos require Da'as. If one separated for him without his Da'as, he was not Yotzei. Therefore, it is as if the Mudar takes the Madir's money to pay a debt. One opinion forbids the Mudar to return the Madir's Aveidah, for it exempts him from giving Tzedakah (while engaged with the Aveidah), even though the Madir does not lose! The other opinion permits only because it is uncommon to save money through this. It is not Mavri'ach Ari (merely preventing potential damage) because the Mudar takes the Madir's property. Even if something does not require Shelichus, if the Mudar commands the Madir, he may not do it. It does not need Da'as because it is Zechus, and Stam we assume that he wants it.

Question (Tosfos Kidushin 41b DH Nafka): A verse teaches that the Kohen Gadol must own the bull he offers on Yom Kipur. This implies that for other Korbanos, one may offer another's Korban. Why can't we learn Shelichus for all Korbanos from here?

Answer (Tosfos): The Kohen Gadol's bull is a Chatas. "Oso" teaches that we may offer a Chatas for Ploni against his will. Therefore, Shelichus works for Chatas.

Igros Moshe (Kodshim 9 (OC 1 p.360)): If a thief stole Levi's Korban and slaughtered it in the Mikdash l'Shem Levi, is as if he returned the animal. We cannot consider this like Levi's action through Shelichus, since he did not know about it. Zachin l'Adam she'Lo b'Fanav does not apply, for it is not Zechus (Levi lost the Mitzvah of Semichah). Rather, we must say that others can slaughter his Korban b'Al Korcho without Shelichus; as long as we did not hear that Levi does not want to get Kaparah. Tosfos holds that Shelichus is needed. Tosfos must explain that since now Levi will not be able to do Semichah in any case, it is Zechus for him that the Korban be Kosher. Zachin l'Adam applies, so the thief is considered Levi's Shali'ach. Olah and Shelamim are Kosher even when they do not atone. If a convert had an Olah or Shelamim and died without heirs, we offer it. It is not clear whether it helps to offer it for a person who did not agree to offer it.

Poskim

Rema (OC 128:10): (When calling the Kohanim to give Birkas Kohanim,) the Shali'ach Tzibur says "Am Kedoshecha."

Beis Yosef (Sof Siman 127 DH Kosav): One should not say "Kohanei Am Kedoshecha", for they are not Kohanim of Yisrael, rather, of Hash-m. One can say "Kohanim Am Kedoshecha", similar to "u'Vnei Aharon Am Kedoshecha" in the Viduy of Yom Kipur. The text of Rav Amram Gaon, Rav Sadya Gaon and the Rambam (Sof Hilchos Tefilah) is Kohanim Am Kedoshecha.

Hagahos (in Tur ha'Shalem 11): Some editions say that this is from Bedek ha'Bayis. Really, it is a Hagahah in the Beis Yosef, like Shirei Keneses ha'Gedolah and Mor u'Ktzi'ah say.

Magen Avraham (3): Sefer Chasidim (805; this is not in our texts of Sefer Chasidim) says that 'Kohanim Am' is not a Semichus (it does not mean 'the Kohanim of Am Yisrael'). We hold that they are Hash-m's Sheluchim. Rather, they are called "Am Kodshecha", even though they are not called just "Am" (Yoma 41b).

Pri Chodosh (2, cited in Eshel Avraham 3): The Gemara in Yoma (41b and 66a) says that Kohanim are called Am Kedoshecha.