It is a famous result proved by Izumi-Longo-Popa that if a compact group G acts on a factor M, which has a separable predual, and if this action is minimal, then every intermediate subfactor N between M and M^G has a form of a fixed point algebra M^H for some closed subgroup H of G. It is also well known as a duality result that when M is a factor with an outer action of a discrete group G, then every intermediate subfactor N between M and its crossed product by G has a form of crossed product by some subgroup H of G. These one to one correspondences between the set of subgroups and the set of intermediate subfactors are called Galois correspondence. In the case of C*-algebra, a Galois correspondence for finite group actions on separable simple C*-algebras was proved by Izumi in 2001. And recently, Cameron and Smith showed a Galois correspondence for discrete group actions on simple C*-algebras. In this seminar, I will talk about a Galois correspondence for isometrically shift-absorbing actions of compact groups on separable simple nuclear C*-algebras.