The Lenstra map on classifying spaces and G-theory of group rings
Let G be a finite group, R a Noetherian ring, and \(G_*(RG)\) the Quillen K-theory of the category of finitely generated RG-modules, where RG is the group ring of G with coefficients in R. H. Lenstra has derived an ingenious formula for \(G_ 0(RG)\) when G is abelian, and the author generalized Lenstra's work to compute \(G_ n(RG)\), \(n\geq 1\), for abelian G and many R (including \(R={\mathbb{Z}})\). In this paper the author lifts Lenstra's construction to a functor on the level of classifying spaces which is a homotopy equivalence. This allows him to improve his earlier results by including more general coefficient rings R and some non- abelian groups G (for example, dihedral groups).
scientific article; zbMATH DE number 3947211