We compare representations of the real and complex general linear groups and special linear groups in the framework of -theory, using base change on -parameters. We introduce a notion of base change on -theory involving the fixed point set of the reduced dual of a complex group. For general linear groups, we prove that the base change map is compatible with the Connes–Kasparov isomorphism.
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Kuok Fai Chao, Hang Wang, Langlands functorality in -theory for -algebras. I. Base change. J. Noncommut. Geom. 11 (2017), no. 3, pp. 1001–1036DOI 10.4171/JNCG/11-3-7