Equivariance and imprimivity 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 submultiplicative unitary of V with quotient U. We define notions for right-Hilbert bimodules of coactions of S_V and Ŝ_V, their restrictions to S_W and Ŝ_U, their dual coactions, and their full and reduced crossed products. If N(A) denotes the imprimitivity bimodule associated to a coaction δ of S_V on a C*-algebra A by Ng's imprimitivity theorem, we prove that for a suitably nondegenerate injective right-Hilbert bimodule coaction of S_V on _AX_B, the balanced tensor products N(A) ⊗ _{A × ŜW} (_AX_B × Ŝ_W) and (_AX_B × Ŝ_V x_r S_U) ⊗ _{B × ŜV xrSU} N(B) are isomorphic right-Hilbert A × Ŝ_V xr S_U - B × Ŝ_W bimodules. This can be interpreted as a natural equivalence between certain crossed-product functors.