La formule des traces locale tordue

The local trace formula gives strong relations between two types of invariant distributions on a reductive group defined over a local field: orbital integrals and characters of representations. For connected reductive groups, the formula was proved by J. Arthur. We extend the formula to twisted spaces, that is, roughly speaking, to non-connected reductive groups. The formula has the same consequences as in the connected case. In particular, we compute the elliptic product of tempered elliptic twisted representations.