Twistings, crossed coproducts, and Hopf-Galois coextensions

Let H be a Hopf algebra. Ju and Cai (2000) introduced the notion of twisting of an H-module coalgebra. In this paper, we study the relationship between twistings, crossed coproducts, and Hopf-Galois coextensions. In particular, we show that a twisting of an H-Galois coextension remains H-Galois if the twisting is invertible.