On the Farrell–Jones conjecture for localising invariants

Abstract

We prove the Farrell–Jones conjecture for fifinitary localising invariants with coefficients in left-exact ∞-categories for finitely ℱ-amenable groups and, more generally, Dress-FarrellHsiang-Jones groups. Our result subsumes and unifies ments for the K-theory of additive categories and spherical group rings and extends it for example to categories of fect modules over E1-ring spectra.