On compact Kähler orbifold

In this paper, we study compact complex orbifolds. In the first part, we shows the equivalence of two notions of compact Kähler orbifold. In the second part, we shows various versions of Demailly’s regularisation theorems for compact orbifold and study the positivity of orbifold vector bundle. In the last section, we give a version of equivariant GAGA communicated to us by Brion.