Let e : Nn → Mm be an embedding of closed, ori- ented manifolds of dimension n and m respectively. We study the relationship between the homology of the free loop space LM on M and of the space LNM of loops of M based in N and define a shriek map H∗(e)! : H∗(LM, Q) → H∗(LNM, Q) using Hochschild cohomology and study its properties. In particular we extend a result of F ́elix on the injectivity of the map induced by aut1 M → map(N, M; f) on rational homotopy groups when M and N have the same dimension and f : N → M is a map of non zero degree.