On the Borel cohomology of free loop spaces - Ottesen, Iver (MATHEMATICA SCANDINAVICA, 2003)
Let X be a space and let K = H^*(X; F_p) where p is an odd prime. We construct functors Ω and which approximate cohomology of the free loop space Λ X as follows: There are homomorphisms Ω(K) → H^*(Λ X; F_p) and (K)→ H^*(ET×_TΛ X;F_p). These are isomorphisms when X is a product of Eilenberg-MacLane spaces of type K(F_p,n) for n ≥ 1.