  We study the phase diagram and critical behavior of a two-dimensional lattice
SO($N_c$) gauge theory ($N_c \ge 3$) with two scalar flavors, obtained by
partially gauging a maximally O($2N_c$) symmetric scalar model. The model is
invariant under local SO($N_c$) and global O(2) transformations. We show that,
for any $N_c \ge 3$, it undergoes finite-temperature
Berezinskii-Kosterlitz-Thouless (BKT) transitions, associated with the global
Abelian O(2) symmetry. The transition separates a high-temperature disordered
phase from a low-temperature spin-wave phase where correlations decay
algebraically (quasi-long range order). The critical properties at the
finite-temperature BKT transition and in the low-temperature spin-wave phase
are determined by means of a finite-size scaling analysis of Monte Carlo data.
