I run into a note by Vasily Krylov's note on slices.

$\gdef\Gr{\mathcal{Gr}}$ There are two key new ideas,

• one is that $\Gr$ is $Bun_G(\P^1)$ with a trivialization on $\P^1 \RM 0$
• the other is that, there is a $\C^*_t$-action on $\Gr$, either viewed as rotation $z$, as $G((z) )/G[[z] ]$, or viewed as acting on the domain $\P^1$. The limit that $t \to 0$ is like zooming in at $z=0$, and $t \to \infty$ is zooming in at $z=\infty$. We have $$(\Gr)^{\C^*_t} = \sqcup_{\mu \in \Lambda_+} G z^\mu$$ where $\Lambda_+$ is the dominant cocharacters in $T \In G$.