  Deformed special relativity is embedded in deformed general relativity using
the methods of canonical relativity and loop quantum gravity. Phase-space
dependent deformations of symmetry algebras then appear, which in some regimes
can be rewritten as non-linear Poincare algebras with momentum-dependent
deformations of commutators between boosts and time translations. In contrast
to deformed special relativity, the deformations are derived for generators
with an unambiguous physical role, following from the relationship between
canonical constraints of gravity with stress-energy components. The original
deformation does not appear in momentum space and does not give rise to
non-locality issues or problems with macroscopic objects. Contact with deformed
special relativity may help to test loop quantum gravity or restrict its
quantization ambiguities.
