  We extend Donaldson's asymptotically holomorphic techniques to symplectic
orbifolds. More precisely, given a symplectic orbifold such that the symplectic
form defines an integer cohomology class, we prove that there exist sections of
large tensor powers of the prequantizable line bundle such that their zero sets
are symplectic suborbifolds. We then derive a Lefschetz hyperplane theorem for
these suborbifolds, that computes their real cohomology up to middle dimension.
We also get the hard Lefschetz and formality properties for them, when the
ambient manifold satisfies those properties.
