The reduced C1-algebra of the p-adic group GL(n)

The reduced C¹-algebra of the p-adic group GL(n) is Morita equivalent to an abelian C¹-algebra. The structure of this abelian C¹-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.