The Baum-Connes assembly map, delocalization and the Chern character

For a discrete group Γ, we explicitly describe the rational Baum-Connes assembly map in “homological degree ?2” and show that in this domain it factors through the algebraic K-theory of the complex group ring of Γ. We also state and prove a delocalization property for , namely expressing it rationally in terms of the Novikov assembly map. Finally, we give a handicrafted construction of the delocalized equivariant Chern character (in the analytic language) and prove that it coincides with the equivariant Chern character of Lück (Invent. Math. 149 (2002) 123-152) (defined in the topological framework).