  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.
