La C *-algèbre d'une quasi-représentation

Abstract

We show that the C * -algebra of the regular representation of a discrete group G onto a subset Σ of G is the reduced C * -algebra of an r-discrete groupoid whose space of units is totally disconnected and contains Σ as a dense subset. The C *-algebra of quasicrystals, some Cuntz-Krieger and crossed product algebras, and Wiener-Hopf algebras are particular cases of this construction