 antispherical functor* is the functor $$\operatorname{ASph}:=  (\cM^{(0)}_{\overline{\bbF}_q}\otimes_{Z(\cH^{(0)}_{\overline{\bbF}_q})}\bullet)\circ S^{-0}:$$ $$\xymatrix{ \operatorname{SP}_{\mathbf{\whG}