In Langlands conjectures, functoriality is a far-reaching principle, with implications in representation theory, number theory and beyond. In this talk we investigatem base change and automorphic induction, two examples of functoriality, at the level of K-theory for the reduced C*-algebra of GLn(R). As an application, the resemblance between the K-groups of C*_rGL2n(R) and C*_rGLn(C) will be interpreted using automorphic induction.

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Functoriality, Langlands correspondence, Group C*-algebra