Produit de Chas-Sullivan et actions d'un groupe de Lie connexe

Let Γ be a connected Lie group, X be Γ-space and EΓ=EΓ×ΓX the associated homotopy quotient. In this short note, we explain how rational homotopy theory provides explicit computations of the loop product on EΓ and we construct an example where this product is trivial or not depending on the given action.