Abstract

For an almost normal subgroup Γ₀ of a discrete group Γ, conditions are given which allow one to define a universal C^*-norm on the Hecke algebra H(Γ,Γ₀). If Γ is a semidirect product of a normal subgroup N containing Γ₀ by a group G satisfying some order relations arising from a naturally defined subsemigroup T, and if the normalizer of N is also normal in Γ, then a presentation of H(Γ,Γ₀) is given. In this situation the C^*-completion of H(Γ,Γ₀) is *-isomorphic with the semigroup crossed product C^*-algebra C^*(N ∕ Γ₀) ⋊ T.

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