J.~Arthur put the trace formula in invariant form for all connected reductive groups and certain disconnected ones. However his work was written so as to apply to the general disconnected case, modulo two missing ingredients. This paper supplies one of those missing ingredients, namely an argument in Galois cohomology of a kind first used by D.~Kazhdan in the connected case.

MSC Classifications:

22E50, 11S37, 10D40 show english descriptions Representations of Lie and linear algebraic groups over local fields [See also 20G05]
Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
unknown classification 10D40 22E50 - Representations of Lie and linear algebraic groups over local fields [See also 20G05]
11S37 - Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E50]
10D40 - unknown classification 10D40

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