  Stacks were introduced by Grothendieck and Giraud and are, roughly speaking,
sheaves of categories. Kashiwara developed the theory of twisted modules, which
are objects of stacks locally equivalent to stacks of modules over sheaves of
rings. In this paper we recall these notions, and we develop the formalism of
operations for stacks of twisted modules. As an application, we state a twisted
version of an adjunction formula which is of use in the theory of integral
transforms for sheaves and D-modules.
