Invariance under twisting for crossed products

Abstract: We prove a result of the type ''invariance under twisting'' for Brzezinski's crossed products, as a common generalization of the invariance under twisting for twisted tensor products of algebras and the invariance under twisting for quasi-Hopf smash products. It turns out that this result contains also as a particular case the equivalence of crossed products by a coalgebra (due to Brzezinski).