The four-lepton decay mode of the Higgs boson allows for a clean kinematic reconstruction, thereby enabling precision studies of the Higgs boson properties and of its production dynamics. We compute the NNLO QCD corrections to fiducial cross sections relevant to this decay mode in the gluon-fusion production of a Higgs boson in association with a hadronic jet, and study the impact of the QCD corrections on the fiducial acceptance factors in inclusive Higgs and Higgs-plus-jet production. We investigate in detail the different definitions used in the ATLAS and CMS measurements to define the fiducial cross sections. Differences in the lepton isolation prescription are found to have a sizeable impact on the higher order corrections to the fiducial acceptance factors.
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