Representations of hermitian kernels by means of Krein spaces. II. Invariant kernels

In this paper we study hermitian kernels invariant under the action of a se migroup with involution. We characterize those hermitian kernels that reali ze the given action by bounded operators on a Krein space. This is motivate d by the GNS representation of *-algebras associated to hermitian functiona ls, the dilation theory of hermitian maps on C*-algebras, as well as others . We explain the key role played by the technique of induced Krein spaces a nd a lifting property associated to them.