It is proved that Kaygun’s Hopf-Hochschild cochain complex for a module-algebra is a brace algebra with multiplication. As a result, an analogue of Deligne’s Conjecture holds for module-algebras, and the Hopf-Hochschild cohomology of a module-algebra has a Gerstenhaber algebra structure.
"Operations on the Hopf-Hochschild complex for module-algebras." Homology Homotopy Appl. 13 (1) 259 - 272, 2011.