We have studied the uJy radio properties of K-selected galaxies detected in the Ultra-Deep Survey portion of UKIDSS using 610- and 1,400-MHz images from the VLA and GMRT. These deep radio mosaics, combined with the largest and deepest K image currently available, allow high-S/N detections of many K-selected sub-populations, including sBzK and pBzK star-forming and passive galaxies. We find a strong correlation between the radio and K fluxes and a linear relationship between SFR and K luminosity. We find no evidence, from either radio spectral indices or a comparison with submm-derived SFRs, that the full sample is strongly contaminated by AGN. The sBzK and pBzK galaxies have similar levels of radio flux, SFR and specific SFR (SSFR) at z < 1.4, suggesting there is strong contamination of the pBzK sample by star-forming galaxies. At z > 1.4, pBzK galaxies become difficult to detect in the radio stack, though the implied SFRs are still much higher than expected for passively evolving galaxies. Their radio emission may come from low-luminosity AGN. EROs straddle the passive and star-forming regions of the BzK diagram and also straddle the two groups in terms of their radio properties. K-bright ERO samples are dominated by passive galaxies and faint ERO samples contain more star-forming galaxies. The star-formation history (SFH) from stacking all K sources in the UDS agrees well with that derived for other wavebands and other radio surveys, at least out to z ~ 2. The radio-derived SFH then appears to fall more steeply than that measured at other wavelengths. The SSFR for K-selected sources rises strongly with redshift at all stellar masses, and shows a weak dependence on stellar mass. High- and low-mass galaxies show a similar decline in SSFR since z ~ 2 (abridged).
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