Let k be an algebraically closed field of characteristic p>0 and R be a suitable valuation ring of characteristic 0, dominating the Witt vectors W(k). In this talk we show how Lubin-Tate formal groups can be used to lift those order p^n automorphisms of k[[Z]] to R[[Z]], which occur as endomorphisms of a formal group over k of suitable height We also describe the fixed point geometry of such automorphisms. This result can be applied to prove the existence of smooth liftings of Galois covers of smooth curves from characteristic p to characteristic 0, provided the p-part of the inertia groups acting on the completion of the local rings at the points of the cover over k are p-power cyclic and determined by an endomorphism of a suitable formal group over k.