  We define a new cohomology set for an affine algebraic group G and a
multiplicative finite central subgroup Z, both defined over a local field of
characteristic zero, which is an enlargement of the usual first Galois
cohomology set of G. We show how this set can be used to normalize the
Langlands-Shelstad endoscopic transfer factors and to give a conjectural
description of the internal structure and endoscopic transfer of L-packets for
arbitrary connected reductive groups that extends the well-known conjectural
description for quasi-split groups. In the real case, we show that this
description is correct using Shelstad's work.
