On SGn of orders

AbstractThe main result of the paper is: If R is a Dedekind domain with field of fractions K, and M is an R-order in a separable K-algebra A, then, under certain conditions on R and M, SGn(M) = ker(Gn(M) → Gn(A)) = 0 for all n⩾ 1. In particular, this theorem applies to the integral group ring of a finite group G. If M is regular, e.g., if M is maximal, then SKn(M) = 0