\end{aligned}$$ where $\widetilde{R\iota_{\ast}\mathcal{F}}$ is the unique element in $D_{c}^{b}(K\times_{K_L}X_G,K)$ satisfying $p^{\ast}(R{\iota}_{\ast}\mathcal{F})=\mu^{\ast}(\widetilde{R\iota_{\ast}\mathcal{F}})$. 