Let pbe a prime number and  be any finite Galois p-extension of function fields of one variable with field of constants k, an algebraically closed field of characteristic p. In this paper, we obtain the Galois module structure of  the module generated by the differentials fixed by the action of the Cartier operator whose poles are contained in the support of the modulus  of L, which is induced by an arbitrary divisor  in K, and of  the module of the differentials fixed by the action of the Cartier operator. That is,   we obtain explicitly the decomposition of  and of  as a direct sum of indecomposable -modules and -modules, respectively, for any divisor in Linduced by a divisor  in K.

Galois modules, injective modules, differentials, semisimple differentials, holomorphic differentials, modular representation.