Representations and K-theory of Discrete Groups
Alejandro Adem
ABSTRACT: Let be a discrete group of finite virtual cohomological
dimension with certain finiteness conditions of the type satisfied
by arithmetic groups. We define a representation ring for $\Gamma$
determined on its elements of finite order which is of finite type.
Then we determine the contribution of this ring to the topological
$K$-theory $K^*(B\Gamma)$,obtaining an exact formula for the
difference in terms of the cohomology of the centralizers of
elements of finite order in $\Gamma$.