Central motives

Central sheaves were introduced by Gaitsgory in order to geometrize the identification of the center of the Iwahori-Hecke algebra and the spherical Hecke algebra. This concept is an important step towards Bezrukavnikov's equivalence. After a wrap-up concerning the motivic Satake equivalence, I will talk about a motivic approach to a central sheaves functor. This is joint work with Robert Cass and Thibaud van den Hove.