Groups acting amenably on their Higson corona

We investigate groups that act amenably on their Higson corona (also known as bi-exact groups) and provide reformulations of this in relation to the stable Higson corona, nuclearity of crossed products and to positive type kernels.We further investigate implications of this in relation to the Baum-Connes conjecture, and prove that Gromov hyperbolic groups have isomorphic equivariant K -theories of their Gromov boundary and their stable Higson corona.1. Introduction 45 2. Bi-exact groups 47 3. Amenable actions on the Higson compactification 49 3.1.The commutative case 49 3.2.Groups acting amenably on the stable Higson compactification and stable Higson corona 51 3.3.The case of the reduced algebras 56 3.4.Nuclearity of crossed products and positive type kernels 57 4. Isomorphism results 60 References 65 Financial support was provided by the Deutsche Forschungsgemeinschaft DFG through the Priority Programme SPP 2026 "Geometry at Infinity" (EN 1163/5-1