Title: Rational injectivity of the Farrell-Jones assembly map for algebraic K-theory

Abstract: A consequence of the Farrell-Jones Conjecture says that the assembly map from the equivariant homology theory $H_n(\underline{E};K)$ associated to algebraic K-theory and the space of proper $G$-actions  to the algebraic $K$-group $K_n({\mathbb Z}G)$ is rationally bijective. We prove this for groups satisfying some homological finiteness conditions and under a certain number theoretic assumption which is satisfied in certain cases. This result generalizes substantially the proof of Boekstedt-Hsiang-Madsen of the K-theoretic Novikov Conjecture. This is joint work with Holger reich, John Rognes and Marco Varisco.