  A gamma ray burst with strong optical-UV emission occuring in a molecular
cloud will photodissociate H2, photoionize H2, H, and He, and destroy dust
grains. We model these processes, including time-dependent radiative transfer
in both continuum radiation and the resonance lines of H2. The UV will pump H2
into vibrationally-excited levels. We calculate the absorption spectrum
imprinted on radiation from the GRB at various times. In addition to the strong
absorption lines of H2(v=0) at lambda < 1110 Angstrom, due to cold ambient gas,
we find that radiation reaching us from the GRB and its afterglow will show
strong absorption lines due to vibrationally-excited H2 at 1110 < lambda < 1705
Angstrom. These absorption lines, if observed, would provide unequivocal
evidence for association of the GRB with molecular gas. Low-resolution spectra
will exhibit conspicuous features due to clustering of individual lines; a list
of the strongest such absorption features is given for spectral resolution R
approx 350 characteristic of the grism on the Swift UV-Optical Telescope.
