2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/102262Controlled $K$-theory is used to show that algebraic $K$-theory of virtually abelian groups is described by an assembly map defined using possibly-infinite hyperelementary subgroups. The Farrell-Jones summand (coming from infinite subgroups) is parameterized by the rational projective space of the group, and a reduced version is torsion. Includes general material on assembly and universal spaces.30 page AMS-TeX file. Feb 06 revision fixes misprints, minor errorsK-Theory and HomologyGeometric Topology19A31; 19B28; 19DXXtext