On Azumaya skew group rings

Let S be a ring with 1, G a finite automorphism group of S, S-G the subring of the elements fixed under each element in G, C the center of S, and S * G the skew group ring of G over S with center Z (not necessarily C-G). Assume the order of G is a unit in S. Then S * G is an Azumaya Z-algebra if and only if S is a G-Galois extension of S-G and (S * G)(G') is an Azumaya algebra, where G' is the inner automorphism group of S * G induced by G. Moreover, when S is an H-separable extension of S-G, S * G is an Azumaya Z-algebra if and only if S is a G-Galois extension of S-G and S-G is an Azumaya algebra.