We present results from an ongoing Keck spectroscopic survey of red giant stars in a field located along the major axis of M31 , \approx 34 kpc in projection from the nucleus and near the luminous globular cluster G1 . We use multislit LRIS spectroscopy to measure the Ca ii near-infrared triplet in 41 stars ranging in apparent magnitude from 20 < I < 22 . Of these , 23 stars are found to have radial velocities v < -200 km s ^ { -1 } indicating that they are giants in M31 ; the rest are likely to be foreground Galactic dwarf stars . Roughly two-thirds of the M31 members concentrate at v = -451 km s ^ { -1 } , with a relatively small velocity spread [ \sigma ( Gaussian ) = 27 ~ { } km~ { } s ^ { -1 } ] which suggests that they belong to the outer disk or possibly a cold debris trail in the halo . The mean velocity of this group of red giants is consistent with that of nearby neutral hydrogen and models of the velocity field of M31 ’ s disk , rather than with G1 or the systemic velocity of M31 . We use V,I photometry to estimate a mean metallicity of \langle [ Fe / H ] _ { phot } \rangle = -0.8 for this group of potential M31 outer disk stars . Six stars out of the 23 M31 member giants have metallicities and velocities consistent with those of G1 ( after accounting for its intrinsic spread in v and [ Fe/H ] ) : one of these stars lies within the projected tidal radius of G1 and is a likely member ; the remaining 5 stars are not physically close to G1 , and may represent tidal debris from G1 . However , more data are needed to confirm the nature of these 5 stars , as it is likely that they simply represent M31 ’ s field halo population . We might have expected to detect tidal debris if G1 were the remnant core of a dwarf galaxy being accreted by M31 ; instead , the majority of M31 giants in this field are metal-rich and belong to what is evidently the outer disk of M31 , and only a small fraction ( \lesssim 20 \% ) could possibly have originated in G1 .