Equivariant *-homomorphisms, Rokhlin constraints and equivariant UHF-absorption

We classify equivariant -homomorphisms between C-dynamical systems associated to actions of finite groups on C*-algebras with the Rokhlin property. In addition, the given actions are classified. An obstruction is obtained for the Cuntz semigroup of a C*-algebra allowing such an action. We also obtain an equivariant UHF-absorption result.