On T-folds, G-structures and Supersymmetry

We describe how to calculate the amount of supersymmetry associated to a class of supergravity theories obtained by compactification on T-folds. We illustrate our discussion by calculating the degree of supersymmetry enjoyed by a particular set of massive supergravities which have been obtained in the literature by compactifying type II supergravity on such backgrounds. Our discussion involves a modification of the usual arguments, based upon G-structures, for the amount of supersymmetry preserved by geometric compactifications.