Let $\mathscr{X}$ be a smooth DM-stack with projective coarse moduli space. I am interested in the orbifold cohomology ring $H^\mathrm{orb}(\mathscr{X})$, as defined by Chen-Ruan (for orbifolds) and Abramovich-Vistoli (algebraically). Additively, this is nothing but the ordinary cohomology of the inertia stack, but it has a funny multiplication and a funny grading.

The multiplication I think I can motivate from the point of view of GW theory: if you think (somewhat perversely) of the ordinary multiplication in the cohomology ring of a variety $X$ as arising from 3-pointed genus zero stable maps into $X$, then the multiplication in $H^\mathrm{orb}(\mathscr{X})$ should come from 3-pointed stable orbicurve maps, which it does.

The grading is the part that is a mystery to me. Or rather, I understand that it has the nice properties that the grading of the untwisted sector is the same as the usual one, and that the multiplication preserves the grading.

But I have zero intuition for why the multiplication preserves the grading -- I can read through the proofs, but it looks like magic. Is there any a priori reason to think that this is the "right" grading? I am vaguely aware that physicists have been considering the age grading for some time now, and surely they must have had some reason for this. I also know that the age grading shows up in the Riemann-Roch formula on an orbicurve -- can the age grading and/or its compatibility with the quantum product be motivated from this fact?