# Item

ITEM ACTIONSEXPORT

Released

Conference Paper

#### A K-theoretic Selberg trace formula

##### External Ressource

https://doi.org/10.1007/978-3-030-43380-2_19

(Publisher version)

##### Fulltext (public)

arXiv:1904.04728.pdf

(Preprint), 255KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Mesland, B., Şengün, M. H., & Wang, H. (2020). A K-theoretic Selberg trace formula.
In R. E.. Curto, W. Helton, & H. Lin (*Operator theory,
operator algebras and their interactions with geometry and topology: Ronald G. Douglas memorial volume* (pp. 403-424).
Cham: Birkhäuser.

Cite as: http://hdl.handle.net/21.11116/0000-0007-AD87-E

##### Abstract

Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg
trace formula is an equality arising from computing in two different ways the
traces of convolution operators on the Hilbert space L^2(G/H) associated to
test functions.
In this paper we present a cohomological interpretation of the trace formula
involving the K-theory of the maximal group C*-algebras of G and H. As an
application, we exploit the role of group C*-algebras as recipients of higher
indices of elliptic differential operators and we obtain the index theoretic
version of the Selberg trace formula developed by Barbasch and Moscovici from
ours.