  We describe a calculation of the fully differential cross section for Higgs
boson production in the gluon fusion channel through next-to-next-to-leading
order (NNLO) in perturbative QCD. The decay of the Higgs boson into two photons
is included. Technical aspects of the computation are discussed in detail. The
implementation of the calculation into a numerical code, called FEHiP, is
described. The NNLO K-factors for completely realistic photon acceptances and
isolation cuts, including those employed by the ATLAS and CMS collaborations,
are computed. We study various distributions of the photons from Higgs decay
through NNLO.
