Singular coefficients in the $K$–theoretic Farrell–Jones conjecture

Abstract

Let $G$ be a group and let $k$ be a field of characteristic zero. We prove that if the Farrell–Jones conjecture for the $K$–theory of $R\left[G\right]$ is satisfied for every smooth $k$–algebra $R$, then it is also satisfied for every commutative $k$–algebra $R$.