On the K-Theory of the Reduced C*-Algebras of GL(n,R) and GL(n,C) - Mendes, S. (Springer Proceedings in Mathematics & Statistics: APPLIED AND COMPUTATIONAL MATRIX ANALYSIS, 2017)
Using Harish-Chandra’s parameter space, an explicit formula for the K-theory of the reduced C* -algebras of GL(n,C) is obtained, in analogy with the real case GL(n,R) [8]. Applying automorphic induction, an instance of Langlands functoriality principle, we then relate the K-theory of C*_r GL(2n,R) andC*_r GL(n,C).