Author: Caroline Lassueur Title: The Dade Group of a finite group Abstract: The aim of this paper is to construct an equivalent of the Dade group of a p-group for an arbitrary finite group G, whose elements are equivalences classes of endo-p-permutation modules. To achieve this goal we use the theory of relative projectivity with respect to a module and that of relative endotrivial modules. Status: appeared in Journal of Pure and Applied Algebra, vol. 217, Issue 1, pp. 97-113, 2013.