  In this paper we construct the action describing dynamics of the particle
moving in curved spacetime, with a non-trivial momentum space geometry. Curved
momentum space is the core feature of theories where relative locality effects
are presents. So far aspects of nonlinearities in momentum space have been
studied only for flat or constantly expanding (De Sitter) spacetimes, relying
on the their maximally symmetric nature. The extension of curved momentum space
frameworks to arbitrary spacetime geometries could be relevant for the
opportunities to test Planck-scale curvature/deformation of particles momentum
space. As a first example of this construction we describe the particle with
kappa-Poincar\'e momentum space on a circular orbit in Schwarzschild spacetime,
where the contributes of momentum space curvature turn out to be negligible.
The analysis of this problem relies crucially on the solution of the soccer
ball problem.
