“Spaces over a Category and Assembly Maps in Isomorphism Conjectures in K-and L-Theory” by

We give a unified approach to the Isomorphism Conjecture of Farrell and Jones on the algebraic Kand L-theory of integral group rings and to the Baum-Connes Conjecture on the topological K-theory of reduced group C∗-algebras. The approach is through spectra over the orbit category of a discrete group G. We give several points of view on the assembly map for a family of subgroups and describe such assembly maps by a universal property generalizing the results of Weiss and Williams to the equivariant setting. The main tools are spaces and spectra over a category and the study of the associated generalized homology and cohomology theories and homotopy limits.