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 . Mathematics Subject Classification(2000). 22D25, 22D10, 46L80.