  Given a finite unbranched covering of a nonsingular projective scheme we
analyse the morphism between moduli spaces of sheaves induced by pullback. We
have a closer look at cyclic coverings and, in particular, at canonical
coverings of surfaces. Our main application is the construction of Lagrangian
subvarieties of certain irreducible holomorphically symplectic manifolds that
arise from moduli spaces of sheaves on K3 or abelian surfaces.
