2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/231398We investigate base change $C/R$ at the level of $K$-theory for the general linear group $GL(n,R)$. In the course of this study, we compute in detail the $C*$-algebra $K$-theory of this disconnected group. We investigate the interaction of base change with the Baum-Connes correspondence for $GL(n,R)$ and $GL(n,C)$. This article is the archimedean companion of our previous article in the Journal of Noncommutative Geometry.17 pages, introduction and section 5 completely rewrittenK-Theory and HomologyRepresentation Theory46L80; 22D10text