  We view the moduli space of semistable sheaves on a K3 surface as a global
quotient stack, and compute its cotangent complex in terms of the universal
sheaf on the Quot scheme. Relevant facts on the classical and reduced Atiyah
classes are reviewed. We also define the notion of a symplectic stack, and show
that it includes all moduli stacks of semistable sheaves on K3 surfaces.
