  Angular momentum at null infinity has a supertranslation ambiguity from the
lack of a preferred Poincar\'e group and a similar ambiguity when the
center-of-mass position changes as linear momentum is radiated. Recently, we
noted there is an additional one-parameter ambiguity in the possible
definitions of angular momentum and center-of-mass charge. We argue that this
one-parameter ambiguity can be resolved by considering the generalized BMS
charges that are constructed from local 2-sphere-covariant tensors near null
infinity; these supertranslation-covariant charges differ from several
expressions currently used. Quantizing angular momentum requires a
supertranslation-invariant angular momentum in the center-of-mass frame. We
propose one such definition of angular momentum involving nonlocal quantities
on the 2-sphere, which could be used to define a quantum notion of
general-relativistic angular momentum.
