  We investigate groups that act amenably on their Higson corona (also known as
bi-exact groups) and we 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.
