Some interesting formulas in geometric representation theory can be deduced by formally writing down the equivariant localization formula on some moduli space, even though it may be infinite dimensional, singular, or noncompact. One example, explained by Segal, is that localization on the affine Grassmannian produces the Kac-Character formula for affine lie algebras (the simplest example is the Jacobi triple product). I'll explain a new "projection formula," which circumvents the technical difficulties of several of these problems, by embedding the moduli space in an infinite-dimensional ind-Grassmannian. I'll present conditions for when this formula holds, and show that the general question boils down to switching two limits.