  We introduce operator definitions for virtual photon fragmentation functions,
which are needed for reliable calculations of Drell-Yan transverse momentum
($Q_T$) distributions when $Q_T$ is much larger than the invariant mass $Q$. We
derive the evolution equations for these fragmentation functions. We calculate
the leading order evolution kernels for partons to fragment into a unpolarized
as well as a polarized virtual photon. We find that fragmentation functions to
a longitudinally polarized virtual photon are most important at small $z$, and
the fragmentation functions to a transversely polarized virtual photon dominate
the large $z$ region. We discuss the implications of this finding to the
J/$\psi$ mesons' polarization at large transverse momentum.
