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We construct an fpqc gerbe 
$\mathcal {E}_{\dot {V}}$ over a global function field F such that for a connected reductive group G over F with finite central subgroup Z, the set of 
$G_{\mathcal {E}_{\dot {V}}}$-torsors contains a subset 
$H^{1}(\mathcal {E}_{\dot {V}}, Z \to G)$ which allows one to define a global notion of (Z-)rigid inner forms. There is a localization map 
$H^{1}(\mathcal {E}_{\dot {V}}, Z \to G) \to H^{1}(\mathcal {E}_{v}, Z \to G)$, where the latter parametrizes local rigid inner forms (cf. [8, 6]) which allows us to organize local rigid inner forms across all places v into coherent families. Doing so enables a construction of (conjectural) global L-packets and a conjectural formula for the multiplicity of an automorphic representation 
$\pi $ in the discrete spectrum of G in terms of these L-packets. We also show that, for a connected reductive group G over a global function field F, the adelic transfer factor 
$\Delta _{\mathbb {A}}$ for the ring of adeles 
$\mathbb {A}$ of F serving an endoscopic datum for G decomposes as the product of the normalized local transfer factors from [6].
