Twisted equivariant K-theory for proper actions of discrete groups

Abstract

We give a construction for twisted equivariant K-theory in the case of a proper action of a discrete group using twisted bundles. Our construction uses results of Lueck and Oliver to extend a construction of Adem and Ruan. We also show the existence of a Chern character to twisted Bredon cohomology. This gives a partial answer to the question of when you can construct twisted equivariant K-theory out of finite rank twisted bundles.