While it is well known that the moduli space of G-bundles over a smooth projective curve is compact, it is not the case for an arbitrary base variety. This motivated the definition of G-sheaves by Gomez and Sols who proved that their moduli space is a compactification of the moduli space of G-bundles.
In this talk I will study the deformation and obstruction theory of these objects when G is either the symplectic or the orthogonal group. his is joint work with T. Gomez.