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It is a step in the proof of the stabilization of the twisted trace formula.We generalize to the twisted case the proposition 3.1 of the third Arthur'spaper on the stabilization. That is, consider the difference between anomega-equivariant weighted orbital integral (relative to a Levi subspace of atwisted space) and its endoscopic avatar. Then this difference is the ordinaryomega-orbital integral of some function on the Levi subspace. Here, thebase-field is non-archimedean.

Stabilisation de la formule des traces tordue VIII: l'application epsilon_tilde{M} sur un corps de base local non-archim\'edien