  In this article, we consider regular projective arithmetic schemes in the
context of Arakelov geometry, any of which is endowed with an action of the
diagonalisable group scheme associated to a finite cyclic group and with an
equivariant very ample invertible sheaf. For any equivariant morphism between
such arithmetic schemes, which is smooth over the generic fibre, we define a
direct image map between corresponding higher equivariant arithmetic K-groups
and we discuss its transitivity property. Then we use the localization sequence
of higher arithmetic K-groups and the higher arithmetic concentration theorem
developed in \cite{T3} to prove an arithmetic Lefschetz-Riemann-Roch theorem.
This theorem can be viewed as a generalization, to the higher equivariant
arithmetic K-theory, of the fixed point formula of Lefschetz type proved by K.
K\"{o}hler and D. Roessler in \cite{KR1}.

Algebraic Geometry