Title: The extended Brauer quotient of $N$-interior $G$-algebras Authors: Tiberiu Coconet and C.C. Todea; Abstract: We generalize the extended Brauer quotient defined by L. Puig and Y. Zhou in \cite[Section 3]{PuZh} to the case of $N$-interior $G$-algebras, where $N$ is a normal subgroup of a finite group $G$. We use this extended Brauer quotient on permutation algebras to establish some correspondences that generalize known results that hold in the group algebra case. Status: published/2013.