C03 K-theory of group algebras

We will study K-theory of group algebras via assembly maps. A key tool is the Farrell—Jones Conjecture for group rings and its extension to Hecke algebra. We will study in particular integral Hecke algebras, investigate Efimov’s continuous K-theory as an alternative to controlled algebra in the context of the Farrell-Jones conjecture, and study vanishing phenomena for high dimensional cohomology of arithmetic groups.