  Differential inclusive-jet cross sections have been measured in
photoproduction for boson virtualities Q^2 < 1 GeV^2 with the ZEUS detector at
HERA using an integrated luminosity of 300 pb^-1. Jets were identified in the
laboratory frame using the k_T, anti-k_T or SIScone jet algorithms. Cross
sections are presented as functions of the jet pseudorapidity, eta(jet), and
the jet transverse energy, E_T(jet). Next-to-leading-order QCD calculations
give a good description of the measurements, except for jets with low E_T(jet)
and high eta(jet). The cross sections have the potential to improve the
determination of the PDFs in future QCD fits. Values of alpha_s(M_Z) have been
extracted from the measurements based on different jet algorithms. In addition,
the energy-scale dependence of the strong coupling was determined.
