  We report on the experimental realization of a state-dependent lattice for a
two-orbital fermionic quantum gas with strong interorbital spin exchange. In
our state-dependent lattice, the ground and metastable excited electronic
states of $^{173}$Yb take the roles of itinerant and localized magnetic
moments, respectively. Repulsive on-site interactions in conjunction with the
tunnel mobility lead to spin exchange between mobile and localized particles,
modeling the coupling term in the well-known Kondo Hamiltonian. In addition, we
find that this exchange process can be tuned resonantly by varying the on-site
confinement. We attribute this to a resonant coupling to center-of-mass excited
bound states of one interorbital scattering channel.
