  By using the language of cogroupoids, we show that Hopf-Galois objects of a
twisted Calabi-Yau Hopf algebra with bijective antipode are still twisted
Calabi-Yau, and give their Nakayama automorphism explicitly. As applications,
cleft Galois objects of twisted Calabi-Yau Hopf algebras and Hopf-Galois
objects of the quantum automorphism groups of non-degenerate bilinear forms are
proved to be twisted Calabi-Yau.
