Geodesic
The Atiyah--Bott--Lefschetz formula for elliptic complexes on a~manifold with boundary
Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 38 (1990), pp. 119-183

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Elliptic complexes on a manifold with boundary whose differentials are Boutet de Monvel operators are studied. An Atiyah–Bott–Lefschetz type formula is obtained for such complexes. 
@article{INTD_1990_38_a1,
     author = {A. V. Brenner and M. A. Shubin},
     title = {The {Atiyah--Bott--Lefschetz} formula for elliptic complexes on a~manifold with boundary},
     journal = {Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya},
     pages = {119--183},
     publisher = {mathdoc},
     volume = {38},
     year = {1990},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTD_1990_38_a1/}
}
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A. V. Brenner; M. A. Shubin. The Atiyah--Bott--Lefschetz formula for elliptic complexes on a~manifold with boundary. Itogi Nauki i Tekhniki. Seriya Sovremennye Problemy Matematiki. Noveishie Dostizheniya, Tome 38 (1990), pp. 119-183. http://geodesic.mathdoc.fr/item/INTD_1990_38_a1/