We 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
Cβ-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.Comment: 17 pages, introduction and section 5 completely rewritte