On the Farrell-Jones conjecture for localising invariants

Abstract

We show the Farrell-Jones conjecture with coefficients in left-exact ∞-categories for finitely F-amenable groups and, more generally, Dress-Farrell-Hsiang-Jones groups. Our result subsumes and unifies arguments for the K-theory of additive categories and spherical group rings and extends it for example to categories of perfect modules over E 1 -ring spectra.