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We report on the environments, kinematics, and SFH of [OII]-selected objectsin the z=0.4 galaxy cluster A851, using Keck optical spectra. A large fraction(~55%) of cluster [OII] emitters show strong Balmer absorptions (>4A inequivalent width at Hd). These e(a) spectra have been attributed to dustystarburst galaxies, an interpretation supported by our reddening measurements,which show a high frequency of very reddened [EBV>0.5] [OII] emitters. Ourspectral modeling requires starburst ages >1Gyr, shorter than the clustercrossing timescale. We argue that this starburst phase occurs during clusterinfall based on the radial velocity distribution of the cluster [OII] emitters,which present a deficit of systems near the cluster systemic velocity. Thespatial segregation of some redshifted and blueshifted groups stronglyindicates that the accretion was recent. Throughout the cluster, the fractionin [OII] emitters is a strong function of the local galaxy density. Ouranalysis supports previous suggestions that dusty starburst galaxies arise atthe expense of gas-rich spiral galaxies. In addition, we describe a fainter[OII]-emitting population, comprised largely of dwarf galaxies and find an evenstronger suppression of [OII] emission in high density environments among thissubsample, indicative of more effective destruction by harassment and/orgas-stripping. Comparison to previous morphological studies, limited to thecore of A851, suggests that galaxy-galaxy interactions may trigger thestarbursts. The high e(a) galaxy fraction in A851 compared to that in thefield, however, suggests that some cluster-specific mechanism, likely relatedto the dynamical assembly of the cluster, also contributes to the high numberof starbursts. (abridged)Comment: 23 pages (LaTeX emulateapj), 20 figures, to appear in ApJ. A version  with high-resolution figures available from the lead autho

Infalling Faint [Oii] Emitters in Abell 851. II. Environment, Kinematics, and Star Formation History