Hecke category actions via Smith-Treumann theory

Let $\mathbf{\text{G}}$ be a simply connected semisimple algebraic group over a field of characteristic greater than the Coxeter number. We construct a monoidal action of the diagrammatic Hecke category on the principal block ${\text{Rep}}_0(\mathbf{\text{G}})$ of $\text{Rep}(\mathbf{\text{G}})$ by wall-crossing functors. This action was conjectured to exist by Riche-Williamson. Our method uses constructible sheaves and relies on Smith-Treumann theory.