  Inclusive jet cross sections in photoproduction for events containing a $D^*$
meson have been measured with the ZEUS detector at HERA using an integrated
luminosity of $78.6 {\rm pb}^{-1}$. The events were required to have a
virtuality of the incoming photon, $Q^2$, of less than 1 GeV$^2$, and a
photon-proton centre-of-mass energy in the range $130<W_{\gamma p}<280 {\rm
GeV}$. The measurements are compared with next-to-leading-order (NLO) QCD
calculations. Good agreement is found with the NLO calculations over most of
the measured kinematic region. Requiring a second jet in the event allowed a
more detailed comparison with QCD calculations. The measured dijet cross
sections are also compared to Monte Carlo (MC) models which incorporate
leading-order matrix elements followed by parton showers and hadronisation. The
NLO QCD predictions are in general agreement with the data although differences
have been isolated to regions where contributions from higher orders are
expected to be significant. The MC models give a better description than the
NLO predictions of the shape of the measured cross sections.
