D02 Exotic crossed products and the Baum–Connes conjecture

The Baum–Connes conjecture on the K-theory of crossed products by group actions on C*-algebras is one of the central problems in noncommutative geometry. The conjecture holds for large classes of groups and has important applications in other areas of mathematics. However, there are groups for which the conjecture fails to be true and in this project we study a new formulation of the conjecture due to Baum, Guentner and Willett which avoids the known counterexamples for the classical one. This involves new exotic crossed product functors which differ from the classical maximal or reduced crossed products.