Stacks in Representation Theory. What is a continuous representation of   an algebraic group ?
  In this note I introduce a new approach to (or rather a new language for) representation theory of groups. Namely, I propose to consider a (complex) representation of a group $G$ as a sheaf on some geometric object (a stack).   This point of view necessarily leads to a conclusion that the standard approach to (continuous) representations of algebraic groups is ideologically inconsistent. I propose a way to modify this approach using sheaves on stacks.   In new version I corrected some misprints and added an explanation how stack's approach is related to Vogan's picture of representations. 
Joseph Bernstein
math.RT