Coefficients for the Farrell–Jones Conjecture

Abstract

We introduce the Farrell–Jones Conjecture with coefficients in an additive category with G-action. This is a variant of the Farrell–Jones Conjecture about the algebraic K- or L-theory of a group ring RG. It allows to treat twisted group rings and crossed product rings. The conjecture with coefficients is stronger than the original conjecture but it has better inheritance properties. Since known proofs using controlled algebra carry over to the set-up with coefficients we obtain new results about the original Farrell–Jones Conjecture. The conjecture with coefficients implies the fibered version of the Farrell–Jones Conjecture.