Equivariant K-theory, wreath products, and Heisenberg algebra

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Given a finite group G and a G-space X, we show that a direct sum FG (X) = ₙ ≥ ₀KGₙ (Xⁿ) admits a natural graded Hopf algebra and λ-ring structure, where Gₙ denotes the wreath product G Sₙ. FG (X) is shown to be isomorphic to a certain supersymmetric product in terms of KG(X) as a graded algebra. We further prove that FG (X) is isomorphic to the Fock space of an infinite dimensional Heisenberg (super)algebra. As one of several applications, we compute the orbifold Euler characteristic e(Xⁿ, Gₙ).