On $\mathsf{G}$-isoshtukas over function fields

In this paper we classify isogeny classes of global $\mathsf{G}$-shtukas over a smooth projective curve $C\mathrm{/}{\mathbb{F}}_q$ (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.