  The propagation of electrons in an orbital multiplet dispersing on a lattice
can support anomalous transport phenomena deriving from an orbitally-induced
Berry curvature. In striking contrast to the related situation in graphene, we
find that anomalous transport for an $L=1$ multiplet on the primitive 2D
triangular lattice is activated by easily implemented on-site and
optically-tunable potentials. We demonstrate this for dynamics in a Bloch band
where point degeneracies carrying opposite winding numbers are generically
offset in energy, allowing both an anomalous charge Hall conductance with sign
selected by off-resonance coupling to circularly-polarized light and a related
anomalous orbital Hall conductance activated by layer buckling.
