  We extend the general-relativistic magnetohydrodynamics (GRMHD) capabilities
of Athena++ to incorporate radiation. The intensity field in each finite-volume
cell is discretized in angle, with explicit transport in both space and angle
properly accounting for the effects of gravity on null geodesics, and with
matter and radiation coupled in a locally implicit fashion. Here we describe
the numerical procedure in detail, verifying its correctness with a suite of
tests. Motivated in particular by black hole accretion in the
high-accretion-rate, thin-disk regime, we demonstrate the application of the
method to this problem. With excellent scaling on flagship computing clusters,
the port of the algorithm to the GPU-enabled AthenaK code now allows the
simulation of many previously intractable radiation-GRMHD systems.
