  We prove a global Torelli theorem for the moduli space of marked triples
(X,m,A), consisting of an irreducible holomorphic symplectic manifold X, a
marking m of its second integral cohomology, and a stable and rigid sheaf A of
Azumaya algebras on the cartesian product X^d, d>0, such that the second Chern
class of A is invariant under a finite index subgroup of the monodromy group of
X. The main example involves the rank 2n-2 sheaf over the cartesian square of
holomorphic symplectic manifolds of K3[n]-type considered in the work of the
first author arXiv:1105.3223. The result will be used in the authors
forthcoming work on generalized deformations of K3 surfaces.
