Representation and duality of unimodular C*-discrete quantum groups

Suppose that D is a C*-discrete quantum group and Do a discrete quantum group associated with D. If there exists a continuous action of D on an operator algebra L(H) so that L(H) becomes a D-module algebra, and if the inner product on the Hilbert space H is D-invariant, there is a unique C*-representation 0 of D associated with the action. The fixed-point subspace under the action of D is a Von Neumann algebra, and furthermore, it is the commutant of theta(D) in L(H).