  We use deep near-infrared and submillimeter observations of three massive
lensing cluster fields, A370, A851, and A2390, to determine the average
submillimeter properties of a K'-selected sample. The 38 Extremely Red Objects
(EROs; I-K'>4) with K'<21.25 have a very significant error-weighted mean
850-micron flux of 1.58 +/- 0.13 mJy. The ERO contribution to the 850-micron
background is 1.88 +/- 0.16 x 10^4 mJy per square degree, or about half the
background light. The 17 Very Red Objects (VROs; 3.5<I-K'<4) are also
significantly detected (1.32 +/- 0.19 mJy), bringing the combined VRO and ERO
contribution to 2.59 +/- 0.19 x 10^4 mJy per square degree. There is a
substantial systematic uncertainty (about a factor of two) in this value due to
field-to-field variation, but even with this uncertainty it is clear that a
large fraction of the 850-micron background arises from red objects. An
analysis of the VRO and ERO number counts shows that half of the population's
850-micron light arises in objects with demagnified magnitudes K'<20 and half
in fainter objects. On the basis of the I-J versus J-K' colors of the galaxies,
the bulk of the submillimeter signal appears to arise from the dusty starburst
galaxies in the red object population rather than from the high-redshift
elliptical galaxies.
