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.