(Non)exotic Completions of the Group Algebras of Isotropy Groups

Abstract Motivated by the problem of characterizing KMS states on reduced C$^*$-algebras étale groupoids, we show that norm these algebras induces a C$^*$-norm group isotropy groups. This coincides with for transformation but, as follows from examples Higson–Lafforgue–Skandalis, it can be exotic already groupoids germs associated actions. We is still one some classes graded in particular, partial actions groups and semidirect products exact amenable