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In the absence of external relata, internal quantum reference frames (QRFs)appear widely in the literature on quantum gravity, gauge theories and quantumfoundations. Here, we extend the perspective-neutral approach to QRF covarianceto general unimodular Lie groups. This is a framework that links internal QRFperspectives via a manifestly gauge-invariant Hilbert space in the form of"quantum coordinate transformations", and we clarify how it is a quantumextension of special covariance. We model the QRF orientations as coherentstates which give rise to a covariant POVM, furnishing a consistent probabilityinterpretation and encompassing non-ideal QRFs whose orientations are notperfectly distinguishable. We generalize the construction of relationalobservables, establish a variety of their algebraic properties and equip themwith a transparent conditional probability interpretation. We import thedistinction between gauge transformations and physical symmetries from gaugetheories and identify the latter as QRF reorientations. The "quantum coordinatemaps" into an internal QRF perspective are constructed via a conditioning onthe QRF's orientation, generalizing the Page-Wootters formalism and a symmetryreduction procedure. We find two types of QRF transformations: gauge induced"quantum coordinate transformations" as passive unitary changes of descriptionand symmetry induced active changes of relational observables from one QRF toanother. We reveal new effects: (i) QRFs with non-trivial orientation isotropygroups can only resolve isotropy-group-invariant properties of othersubsystems; (ii) in the absence of symmetries, the internal perspective Hilbertspace "rotates" through the kinematical subsystem Hilbert space as the QRFchanges orientation. Finally, we invoke the symmetries to generalize thequantum relativity of subsystems before comparing with other approaches.[Abridged]

Perspective-neutral approach to quantum frame covariance for general symmetry groups