  We characterize properties of the so-called repulsive polaron across the
recently discovered orbital Feshbach resonance in alkaline-earth(-like) atoms.
Being a metastable quasiparticle excitation at the positive energy, the
repulsive polaron is induced by the interaction between an impurity atom and a
Fermi sea. By analyzing in detail the energy, the polaron residue, the
effective mass, and the decay rate of the repulsive polaron, we reveal
interesting features that are intimately related to the two-channel nature of
the orbital Feshbach resonance. In particular, we find that the life time of
the repulsive polaron is non-monotonic in the Zeeman-field detuning bewteen the
two channels, and has a maximum on the BEC-side of the resonance. Further, by
considering the stability of a mixture of the impurity and the majority atoms
against phase separation, we show that the itin- erant ferromagnetism may exist
near the orbital Feshbach resonance at appropriate densities. Our results can
be readily probed experimentally, and have interesting implications for the
observation of itinerant ferromagnetism near an orbital Feshbach resonance.
