  This paper expands some of the issues of the paper math.SG/0506449. We
introduce a new technique to produce symplectic manifolds, by taking a
symplectic non-free action of a finite group on a symplectic manifold and
resolving symplectically the singularities of the quotient. We also introduce a
new type of Massey product to detect non-formality. This allows to show the
first example of a non-formal simply connected compact symplectic manifold of
dimension 8.
