  Given a C*-algebra A with a left action of a locally compact quantum group G
on it and a unitary 2-cocycle Omega on \hat G, we define a deformation A_Omega
of A. The construction behaves well under certain additional technical
assumptions on Omega, the most important of which is regularity, meaning that
C_0(G)_Omega\rtimes G is isomorphic to the algebra of compact operators on some
Hilbert space. In particular, then A_\Omega is stably isomorphic to the
iterated twisted crossed product \hat G^{op}\ltimes_\Omega G\ltimes A. Also, in
good situations, the C*-algebra A_\Omega carries a left action of the deformed
quantum group G_\Omega and we have an isomorphism G_\Omega\ltimes A_\Omega\cong
G\ltimes A. When G is a genuine locally compact group, we show that the action
of G on C_0(G)_Omega=C*_r(\hat G;Omega) is always integrable. Stronger
assumptions of properness and saturation of the action imply regularity. As an
example, we make a preliminary analysis of the cocycles on the duals of some
solvable Lie groups recently constructed by Bieliavsky et al., and discuss the
relation of our construction to that of Bieliavsky and Gayral.
