# Enchiridion: Vol. 1 (2015): Cary Malkiewich

Author
Cary Malkiewich (University of Illinois at Urbana-Champaign)

Source Paper
Coassembly and the$K$-theory of finite groups
(arxiv:1503.06504)

Source Paper Abstract
We study the K-theory and Swan theory of the group ring R[G], when G is a finite group and R is any discrete ring or ring spectrum. In this setting, the well-known assembly map for K(R[G]) has a lesser-known companion called the coassembly map. We prove that their composite is the equivariant norm of K(R). As a result, we get a splitting of both assembly and coassembly after K(n)-localization, and an apparently new map from the Whitehead torsion group of G over R to the Tate cohomology of BG with coefficients in K(R).