\] Suppose $\mathcal{F}\in D_{c}^{b}(X_{L},K_{L})$. Then $$CC\left(I_{L}^{G}\mathcal{F}\right)=\sum_{K_L-\mathrm{orbits }~S_L~\mathrm{in}~X_L} \chi_{S_{L}}^{mic}(\mathcal{F})[\overline{T_{K\cdot\iota(S_L)}^{\ast}X_G}]+ \sum_{K-orbits~S\text{~in~}\partial(G\cdot \iota(X_{L}))} \chi_{S}^{mic}(I_{L}^{G}\mathcal{F})[\overline{T_{S}^{\ast}X_G}].$$  Suppose $\mathcal{F}\in D_{c}^{b}(X_{L},K_{L})$ and write $$CC(\mathcal{F})=\sum_{K_{L}-\mathrm{orbits }~S_L~\mathrm{in}~X_{L}} \chi_{S_L}^{mic}(\mathcal{F})[\overline{T_{S