A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds

A vector bundle on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. Nod proved that a vector bundle E on X is finite if and only if there is a finite etale Galois covering q :( X) over tilde -> X and a Gal(q)-module V, such that E is isomorphic to the quotient of (X) over tilde x V by the twisted diagonal action of Gal(q) [Nol], [No2]. Therefore, E is finite if and only if the pullback of E to some finite etale Galois covering of X is trivial. We prove the same statement when X is a compact complex manifold admitting a Gauduchon astheno-Kdhler metric.