  We show that the Bloch states in the conduction band of SrTiO$_3$ arise from
the interplay between highly anisotropic hopping in sub-bands derived from the
Ti $t_{2g}$ orbitals and spin-orbit coupling that mixes these orbitals. Because
of the nearly flat-band characteristics for one of the principal axes, at
sufficiently high doping these Bloch states become unstable with respect to
electron interactions, resulting in Mott-like singlet correlations. These
findings may be relevant to the anomalous electronic properties of SrTiO$_3$,
including its unusual superconductivity.
