An Atiyah–Bott–Lefschetz Theorem for Relative Elliptic Complexes

Relative elliptic theory is a theory of elliptic operators for pairs $(M,X)$ of closed smooth manifolds, where $X$ is a submanifold in $M$. We consider geometric endomorphisms of complexes in this theory and prove an analogue of Atiyah–Bott–Lefschetz fixed-point formula for such endomorphisms.