  We propose a generalization of Verbitsky's global Torelli theorem in the
framework of compact K\"ahler irreducible holomorphically symplectic orbifolds
by adapting Huybrechts' proof (arXiv:1106.5573). As intermediate step needed,
we also provide a generalization of the twistor space and the projectivity
criterion based on works of Campana (arXiv:math/0402243) and Huybrechts
(arXiv:math/0106014) respectively.
