I briefly introduce the recently introduced idea of relativity of locality, which is a
consequence of a non-flat geometry of momentum space. Momentum space
can acquire nontrivial geometrical properties due to quantum gravity effects.
I study the relation of this framework with noncommutative geometry, and the
Quantum Group approach to noncommutative spaces. In particular I'm interested
in kappa-Poincaré, which is a Quantum Group that, as shown by Freidel and Livine,
in the 1+1D case emerges as the symmetry of effective field theory coupled with
quantum gravity, once that the gravitational degrees of freedom are integrated
out. I'm interested in particular in the Lorentz covariance of this model which
is present, but is realized in a nontrivial way. If I still have time, I'll then speak
about an under-course general study of the Lorentz covariance of Relative Locality
models.