We have studied the submillimetre (submm) properties of the following classes of near-infrared (NIR)-selected massive galaxies at high redshifts: BzK-selected star-forming galaxies (BzKs); distant red galaxies (DRGs); and extremely red objects (EROs). We used the SCUBA HAlf Degree Extragalactic Survey (SHADES), the largest uniform submm survey to date. Partial overlap of SIRIUS/NIR images and SHADES in SXDF has allowed us to identify 4 submm-bright NIR-selected galaxies, which are detected in the mid-infrared, 24 micron, and the radio, 1.4 GHz. We find that all of our submm-bright NIR-selected galaxies satisfy the BzK selection criteria, except for one galaxy whose B-z and z-K colours are however close to the BzK colour boundary. Two of the submm-bright NIR-selected galaxies satisfy all of the selection criteria we considered, i.e. they belong to the BzK-DRG-ERO overlapping population, or `extremely red BzKs. Although these extremely red BzKs are rare (0.25 arcmin^{-2}), up to 20 % of this population could be submm galaxies. This fraction is significantly higher than that found for other galaxy populations studied here. Via a stacking analysis, we have detected the 850 micron flux of submm-faint BzKs and EROs in our SCUBA maps. While the contribution of z~2 BzKs to the submm background is about 10--15 % and similar to that from EROs typically at z~1, BzKs have a higher fraction (~30 %) of submm flux in resolved sources compared with EROs and submm sources as a whole. From the SED fitting analysis for both submm-bright and submm-faint BzKs, we found no clear signature that submm-bright BzKs are experiencing a specifically luminous evolutionary phase, compared with submm-faint BzKs. An alternative explanation might be that submm-bright BzKs are more massive than submm-faint ones.
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