On the K-theory of the reduced C*-algebras of GL(n, ℝ) and GL(n, ℂ) - Mendes, S. (Springer Proceedings in Mathematics & Statistics, 2015)
Using Harish-Chandra parameter space , an explicit formula for the K-theory of the reduced C∗-algebra 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∗rGL(2n,R) and C∗rGL(n,C).