Effective models and extension of torsors over a discrete valuation ring of unequal characteristic

Let R be a discrete valuation ring of unequal characteristic with fraction field K which contains a primitive p(2)th root of unity. Let X be a faithfully flat R-scheme and G be a finite abstract group. Let us consider a G-torsor Y(K) -> X(K) and let Y be the normalization of X(K) in Y. If G = Z/p(n)Z, n <= 2, under some hypothesis on X, we attach some invariants to Y(K) -> X(K). If p > 2, we determine, through these invariants, when Y -> X has a structure of torsor which extends that of Y(K) -> X(K). Moreover, we explicitly calculate the effective model (recently defined by Romagny) of the action of G on Y