I will begin by describing a relationship between equivariant cohomology theories and algebraic groups. The motivating example is provided by equivariant K-theory, which is closely related to the multiplicative group. However, the same ideas can be applied in the case of elliptic curves to produce equivariant versions of the Hopkins-Miller theory of topological modular forms (elliptic cohomology). In this latter case, it is possible to use the self-duality of elliptic curves to produce a more elaborate “2-equivariant” theory of elliptic cohomology. In this talk, I will sketch some of these ideas, and describe a relationship between 2-equivariant elliptic cohomology and the theory of loop group representations.