Equivariance and Imprimitivity for Discrete Hopf C * -coactions

Let U , V , and W be multiplicative unitaries coming from discrete Kac systems such that W is an amenable normal submultiplica-tive unitary of V with quotient U. We define notions for right-Hilbert bimodules of coactions of SV andˆSV , their restrictions to SW andˆSU , their dual coactions, and their full and reduced crossed products. If N (A) denotes the imprimitivity bimodule associated to a coaction δ of SV on a C *-algebra A by Ng's imprimitivity theorem, we prove that for a suitably nondegenerate injective right-Hilbert bimodule coaction of SV on AXB , the balanced tensor products N (A) ⊗ A׈S