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The purpose of this paper is to describe a general and simple setting for defining (g, p + q)-string operations on a Poincaré duality space and more generally on a Gorenstein space. Gorenstein spaces include Poincaré duality spaces as well as classifying spaces or homotopy quotients of connected Lie groups. Our presentation implies directly the homotopy invariance of each (g, p + q)-string operation as well as it leads to explicit computations. IntroductionShriek maps play a central role in string topology and its generalizations. Following Dold, various presentations have been given [1,3,5,10,30]. Usually shriek maps are defined in (co)homology for maps f : N → M from a closed oriented n-manifold to a closed oriented m-manifold. Here we will consider shriek maps at the cochain level and in a more general setting.More precisely we work in the category of (left or right) differential graded modules over a differential graded lk-algebra (R, d) (lk is a fixed field), that we call for sake of simplicity the category of (R, d)-modules. Its associated derived category [20] is obtained by formally inverting quasi-isomorphisms, i.e. the homomorphisms of (R, d)-modules that induce isomorphisms in homology and hereafter denoted by in the diagrams. In the derived category the vector space of Y. Félix