C^∗-index of observable algebra in the field algebra determined by a normal group

Let G be a finite group and H a normal subgroup. By D(H; G), we denote the crossed product of C(H) and (Formula presented.), which is only a subalgebra of the quantum double D(G) of G. One can construct a C^∗-subalgebra (Formula presented.) of the field algebra (Formula presented.) of G-spin models, such that (Formula presented.) is a D(H; G)-module algebra. The concrete construction of D(H; G)-invariant subalgebra (Formula presented.) of (Formula presented.) is given. Moreover, the C^∗-index of the conditional expectation (Formula presented.) from (Formula presented.) onto (Formula presented.) is calculated in terms of the quasi-basis for z_H.