  Let $H$ be a Hopf algebra. Ju and Cai introduced the notion of twisting of an
$H$-module coalgebra. In this note, 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.
