## Non-supramenable groups acting on locally compact spaces

### Summary

Summary: Supramenability of groups is characterised in terms of invariant measures on locally compact spaces. This opens the door to constructing interesting crossed product $C^*$-algebras for non-supramenable groups. In particular, stable Kirchberg algebras in the UCT class are constructed using crossed products for both amenable and non-amenable groups.

### Mathematics Subject Classification

43A07, 46L55, 46L35

### Keywords/Phrases

supramenable groups, actions on locally compact spaces, purely infinite C^*-algebras and actions