Given a C∗-algebra A with an action of a locally compact quantum group G on it and a unitary 2-cocycle Ω on Gˆ, we define a deformation AΩ of A. We will be particularly interested in the cases when G is either a genuine group or a group dual. The construction behaves well under the regularity assumption on Ω, meaning that C0(G)Ω⋊G is isomorphic to the algebra of compact operators on some Hilbert space. In particular, then AΩ is stably isomorphic to the iterated twisted crossed product Gop⋊ΩG⋊A. Also, in good situations, the C∗-algebra AΩ carries a left action of the deformed quantum group GΩ and we have an isomorphism GΩ⋊AΩ≅G⋊A. As examples we consider Rieffel’s deformation and deformations by cocycles on the duals of some solvable Lie groups recently constructed by Bieliavsky and Gayral. (Joint work with J. Bhowmick, L. Tuset and A. Sangha.)