Plymen, R. J. (1987) The reduced C*-algebra of the p-adic group GL(n). Journal of Functional Analysis, 72 (1), 1-12. (doi:10.1016/0022-1236(87)90076-0).
Abstract
The reduced C*-algebra of the p-adic group GL(n) is Morita equivalent to an abelian C*-algebra. The structure of this abelian C*-algebra is described in terms of unramified unitary characters of Levi subgroups. The K-groups K0 and K1 are both free abelian of infinite rank. Generators are essentially parametrized by two items of Langlands data.
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