Hyperfiniteness of boundary actions of acylindrically hyperbolic groups

We prove that for any countable acylidrically hyperbolic group G, there exists a generating set S of G such that the corresponding Cayley graph $Γ(G,S)$ is hyperbolic, |∂Γ(G,X)|>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 a class of groups that admit a non-elementary acylindrical action on a hyperbolic space with hyperfinite boundary action.