Transitivity of the ${\mathbb{B}}_{\mathrm{d}\mathrm{R}}^{+}$-loop group action on Schubert cells

For $G$ a connected linear algebraic group over a $p$-adic field, we show that the action of $G({\mathbb{B}}_{\mathrm{d}\mathrm{R}}^{+})$ on each Schubert cell in the ${\mathbb{B}}_{\mathrm{d}\mathrm{R}}^{+}$-affine Grassmannian is transitive in the étale topology on affinoid perfectoids, generalizing a result in the reductive case due to Fargues and Scholze.