 $w=\sigma_{\lambda,\varepsilon}$. Let $x\in {\overline\Tt}_w^F$. Then ${{\mathcal O}}_x^{\theta,{\boldsymbol{G}}}$ is of type D provided one of the following holds:  0.  $x\theta$ is not an involution and ${\boldsymbol{G}}\neq \PSL_0(0), \PSL_0(0)$.  0.  $