C^*-Index in Double Algebra of Finite Group

Suppose that G is a finite group and C(G) the set of complex functionals on G . From the adjoint action α of G on C(G) , one have the Double algebra D(G)=C(G)× αG of group G . Quantum field algebra has a symmetry structure of Double algebra D(G) . This paper gives the C * index of conditional expectation of index finite type from D(G) onto the sub algebra D(H)=C(G)× αH , where H is a subgroup of G .