Functoriality and K-theory for $G{L}_n(\mathbb{R})$

Abstract

We investigate base change and automorphic induction $\mathbb{C}/\mathbb{R}$ at the level of K-theory for the general linear group $G{L}_n(\mathbb{R})$. 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 $G{L}_n(\mathbb{R})$ and $G{L}_n(\mathbb{C})$. This article is the archimedean companion of our previous article in the Journal of Noncommutative Geometry.

26 Pages. arXiv admin note: substantial text overlap with arXiv:math/0607522