On the Cyclic Homology of Hopf Crossed Products

We consider Hopf crossed products of the the type A#_\sigma \mathcal{H}, where $\mathcal{H}$ is a cocommutative Hopf algebra, $A$ is an $\mathcal{H}$-module algebra and $\sigma$ is a “numerical” convolution invertible 2-cocycle on $\mathcal{H}$. we give an spectral sequence that converges to the cyclic homology of A#_\sigma \mathcal{H} and identify the $E^1$ and $E^2$ terms of the spectral sequence.