2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75754We compute rationally the topological (complex) K-theory of the classifying space BG of a discrete group provided that G has a cocompact G-CW-model for its classifying space for proper G-actions. For instance word-hyperbolic groups and cocompact discrete subgroups of connected Lie groups satisfy this assumption. The answer is given in terms of the group cohomology of G and of the centralizers of finite cyclic subgroups of prime power order. We also analyze the multiplicative structure.35 pages Added two references and two sentences after Theorem 0.3K-Theory and HomologyAlgebraic Topology55N15text