  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. [Kal16, Dil23])
which allows us 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
[Dil20].
