  In this paper we classify isogeny classes of global $\mathsf{G}$-shtukas over
a smooth projective curve $C/\mathbb{F}_q$ (or equivalently $\sigma$-conjugacy
classes in $\mathsf{G}(\mathsf{F} \otimes_{\mathbb{F}_q}
\overline{\mathbb{F}_q})$ where $\mathsf{F}$ is the field of rational functions
of $C$) by two invariants $\bar\kappa,\bar\nu$ extending previous works of
Kottwitz. This result can be applied to study points of moduli spaces of
$\mathsf{G}$-shtukas and thus is helpful to calculate their cohomology.
