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 .