AG Lie-Gruppen: S. Echterhoff, Universität Münster: K-Theory for Crossed Products by Bernoulli Shifts (Joint work with Sayan Chakraborty, Julian Kranz and Shintaro Nishikawa)

K-Theory for Crossed Products by Bernoulli Shifts (Joint work with Sayan Chakraborty, Julian Kranz and Shintaro Nishikawa) - Vortragender: Siegfried Echterhoff, Universität Münster - Einladender: Kang Li

Abstract: For a large class of unital $C^*$-algebras $A$, we calculate the $K$-theory of reduced crossed products $A^{otimes G}rtimes_rG$ of Bernoulli shifts by groups satisfying the Baum--Connes conjecture. In particular, we give explicit formulas for finite-dimensional $C^*$-algebras, UHF-algebras, rotation algebras, and several other examples. As an application, we obtain a formula for the $K$-theory of reduced $C^*$-algebras of wreath products $Hwr G$ for large classes of groups $H$ and $G$. Our results are motivated and generalize earlier results of Xin Li about the K-theory of lamplighter groups.