  We present a deep Suzaku observation of H1821+643, an extremely rare example
of a powerful quasar hosted by the central massive galaxy of a rich
cooling-core cluster of galaxies. Informed by previous Chandra studies of the
cluster, we achieve a spectral separation of emission from the active galactic
nucleus (AGN) and the intracluster medium (ICM). With a high degree of
confidence, we identify the signatures of X-ray reflection/reprocessing by cold
and slowly moving material in the AGN's immediate environment. The iron
abundance of this matter is found to be significantly sub-solar (Z~0.4Zsun), an
unusual finding for powerful AGN but in line with the idea that this quasar is
feeding from the ICM via a Compton-induced cooling flow. We also find a subtle
soft excess that can be described phenomenologically (with an additional black
body component) or as ionized X-ray reflection from the inner regions of a high
inclination (i=57 degrees) accretion disk around a spinning (a>0.4) black hole.
We describe how the ionization state of the accretion disk can be used to
constrain the Eddington fraction of the source. Applying these arguments to our
spectrum implies an Eddington fraction of 0.25-0.5, with an associated black
hole mass of 3-6x10^9Msun.
