Finiteness of Higher K -Groups of Orders and Group Rings

In this paper, we prove that if R is the ring of integers in a number field F, A any R-order in a semisimple F-algebra, then K_2n(A), G_2n(A) are finite groups for all positive integers n. Hence, even dimensional higher K- and G-groups of integral grouprings of finite groups are finite. We also show that in odd dimensions, SK_n of integral and p-adic integral grouprings of finite p-groups are also finite p-groups (Received: August 2005)