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