Suppose that D is a $C^*$-discrete quantum group and $D_0$ 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 $ heta$ 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 $ heta$(D) in L(H).