Hyperfiniteness of boundary actions of acylindrically hyperbolic groups

Abstract We prove that, for any countable acylindrically hyperbolic group G, there exists a generating set S of G such that the corresponding Cayley graph (G, S) is hyperbolic, | (G, S) |>2, the natural action of G on (G, S) is acylindrical and the natural action of G on the Gromov boundary (G, S) is hyperfinite. This result broadens the class of groups that admit a non-elementary acylindrical action on a hyperbolic space with a hyperfinite boundary action.