2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100954We construct the moduli of twisted sheaves on a projective variety. Then we generalize known results on the moduli space of usual sheaves on a K3 surface to the twisted case. Thus we consider the non-emptyness, the deformation type and the Fourier-Mukai transformation. As an application of our results, Daniel Huybrechts and Paolo Stellari prove Caldararu's conjecture.14 pages, The proof of Lemma 3.18 is changedAlgebraic Geometry14text