Cyclic cohomology of entwining structures

Abstract: In this paper, we introduce and study a cyclic cohomology theory $H<sup>\bullet_\lambda(A,C,\psi)$ for an entwining structure $(A,C,\psi)$ over a field $k$. We then provide a complete description of the cocycles and the coboundaries in this theory using entwined traces applied to dg-entwining structures over $(A,C,\psi)$. We then apply these descriptions to construct a pairing $ H^{m_\lambda(A,C,\psi)} \otimes H^{n_\lambda(A&#39;,C&#39;,\psi&#39;)} \longrightarrow H^{{m+n}_\lambda(A} \otimes A&#39;, C \otimes C&#39;, \psi \otimes \psi&#39;) $, where $(A,C,\psi)$ and $(A&#39;,C&#39;,\psi&#39;)$ are entwining structures.