Representations and K-theory
of Discrete Groups
AlejandroAdem
ABSTRACT: Let be a discrete group of finite virtual cohomological dime*
*n-
sion with certain finiteness conditions of the type satisfied by arithm*
*etic groups.
We define a representation ring for determined on its elements of fini*
*te order
which is of finite type. Then we determine the contribution of this rin*
*g to the
topological K-theory K (B ),obtaining an exact formula for the differen*
*ce in
terms of the cohomology of the centralizers of elements of finite order*
* in .