An Atiyah–Bott–Lefschetz Theorem for Relative Elliptic Complexes

Abstract 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.