Symmetric structure of field algebra of G-spin models determined by a normal subgroup

Let G be a finite group and H a normal subgroup. D(H; G) is the crossed product of C(H) and CG which is only a subalgebra of D(G), the double algebra of G. One can construct a C*-subalgebra FH of the field algebra F of G-spin models, so that FH is a D(H; G)-module algebra, whereas F is not. Then the observable algebra A(H,G) is obtained as the D(H; G)-invariant subalgebra of FH, and there exists a unique C*-representation of D(H; G) such that D(H; G) and A(H,G) are commutants with each other.