Hyperfiniteness of boundary actions of acylindrically hyperbolic groups

We prove that, for any countable acylindrically hyperbolic group G , there exists a generating set S of G such that the corresponding Cayley graph Γ (G,S) is hyperbolic, |∂ Γ (G,S)|>2 , the natural action of G on Γ (G,S) is acylindrical and the natural action of G on the Gromov boundary ∂ Γ (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.