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In my lecture I would like to discuss 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. This point of view necessarily leads to a conclusion that the standard definition of a (continuous) representations of algebraic groups should be modified. The new approach that I suggest seems to explain the observation by several mathematicians (e.g. by D. Vogan) that when we classify irreducible representations it is better to work with the union of sets of irreducible representations for several forms of the group G than with one set of irreducible representations of G.