Orbifold Riemann–Roch and plurigenera

I give a general formula for the Hilbert series of a polarised $n$-dimensional orbifold (for example, with isolated orbifold points). The result comes from orbifold RR, and so ultimately from equivariant RR (the Atiyah–Singer Lefschetz trace formula); however, the formula is organised so that no Chern or Todd classes appear explicitly, and no Dedekind sums. The formula reduces much of my work over 20 years to a few lines of computer algebra.