Let H be a finite dimensional Hopf algebra over a field k, H^* be the dual Hopf algebra of H, and B be a left H-module algebra with center C. Then B is called a right center H^*-Galois extension of B^H if C is a right H^*-Galois and separable extension of C^H. Such a B is characterized in terms of the smash product B # H and some properties of B # H are obtained.

Hopf Galois extensions, center Galois extensions, center Hopf Galois extensions, smash products, Hirata separable extensions.