  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
$C*$-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.
