  We investigate the effects of Population III stars on the sky-averaged 21-cm
background radiation, which traces the collective emission from all sources of
ultraviolet and X-ray photons before reionization is complete. While UV photons
from PopIII stars can in principle shift the onset of radiative coupling of the
21-cm transition -- and potentially reionization -- to early times, we find
that the remnants of PopIII stars are likely to have a more discernible impact
on the 21-cm signal than PopIII stars themselves. The X-rays from such sources
preferentially heat the IGM at early times, which elongates the epoch of
reheating and results in a more gradual transition from an absorption signal to
emission. This gradual heating gives rise to broad, asymmetric wings in the
absorption signal, which stand in contrast to the relatively sharp, symmetric
signals that arise in models treating PopII sources only. A stronger signature
of PopIII, in which the position of the absorption minimum becomes inconsistent
with PopII-only models, requires extreme star-forming events that may not be
physically plausible, lending further credence to predictions of relatively
high frequency absorption troughs, $\nu_{\min} \sim 100$ MHz. As a result,
though the trough location alone may not be enough to indicate the presence of
PopIII, the asymmetric wings should arise even if only a few PopIII stars form
in each halo before the transition to PopII star formation occurs, provided
that the PopIII IMF is sufficiently top-heavy and at least some PopIII stars
form in binaries.
