  Quantum gravity is expected to introduce quantum aspects into the description
of reference frames. Here we set the stage for exploring how quantum gravity
induced deformations of classical symmetries could modify the transformation
laws among reference frames in an effective regime. We invoke the quantum group
$SU_q(2)$ as a description of deformed spatial rotations and interpret states
of a representation of its algebra as describing the relative orientation
between two reference frames. This leads to a quantization of one of the Euler
angles and to the new paradigm of agency-dependence: space is reconstructed as
a collection of fuzzy points, exclusive to each agent, which depends on their
choice of reference frame. Each agent can choose only one direction in which
points can be sharp, while points in all other directions become fuzzy in a way
that depends on this choice. Two agents making different choices will thus
observe the same points with different degrees of fuzziness.
