THE PRODUCT STRUCTURE OF THE EQUIVARIANT K-THEORY OF THE BASED LOOP GROUP OF SU(2)

Let G=SU(2) and let Ω G denote the space of continuous based loops in G, equipped with the pointwise conjugation action of G. It is a classical fact in topology that the ordinary cohomology H*(Ω G) is a divided polynomial algebra Γ[x]. The algebra Γ[x] can be described as an inverse limit as k→∞ of the symmetric subalgebra in Λ(x1, …, xk), where Λ(x1, …, xk) is the usual exterior algebra in the variables x1, …, xk. We compute the R(G)-algebra …