Daf 47a asks: "Bameh Konin? Rav says "B'kaylov shel koneh." I believe we paskin like this. Does this mean that when making a kinyan sudar, such as when we sell our chometz to the Rav, the sudar must belong to the Rav in order for this kinyan to take effect? Also, when doing the kinyan sudar at a wedding (when the Mesader Kiddushin does this transaction with the mechutanim) whose sudar should be used?
We rule that Sudar is done "b'Keilav Shel Koneh." Therefore the one who is acquiring the object must give the Sudar. However, today we generally do not sell the Chametz to the Rav; rather, we make him a Shaliach to sell our Chametz for us and the Kinyan is made in order to give him the right to be our Shaliach (this is called a "Harsha'ah").
If the Makneh has a Sudar, it suffices for him to be Makneh the Sudar to the Koneh and then for the Koneh to give the Sudar back. Also, many Poskim hold that it suffices to borrow a Sudar for the sake of making a Kinyan.
The Kinyan at the wedding is not for the Mesader Kidushin. Rather, it is one of the responsibilities written in the Tena'im (which are mutual; hence, both sides must make the Kinyan), and in the Kesubah in which the Kalah's side is being Koneh from the Chasan.
D. Zupnik