For a large class of unital -algebras , we calculate the -theory of reduced crossed products of Bernoulli shifts by groups satisfying the Baum-Connes conjecture. In particular, we give explicit formulas for finite-dimensional -algebras, UHF-algebras, rotation algebras, and several other examples. As an application, we obtain a formula for the -theory of reduced -algebras of wreath products for large classes of groups and .
Our results are motivated and generalize earlier results of Xin Li about the K-theory of lamplighter groups.
(joint work with Sayan Chakraborty, Julian Kranz, and Shintaro Nishikawa)
