Context. Aims.We examine the role of rotation on the evolution and chemical yields of very metal-poor stars. Methods.The models include the same physics, which was applied successfully at the solar Z and for the SMC, in particular, shear diffusion, meridional circulation, horizontal turbulence, and rotationally enhanced mass loss. Results.Models of very low Z experience a much stronger internal mixing in all phases than at solar Z. Also, rotating models at very low Z, contrary to the usual considerations, show a large mass loss, which mainly results from the efficient mixing of the products of the 3α reaction into the H-burning shell. This mixing allows convective dredge-up to enrich the stellar surface in heavy elements during the red supergiant phase, which in turn favours a large loss of mass by stellar winds, especially as rotation also increases the duration of this phase. On the whole, the low Z stars may lose about half of their mass. Massive stars initially rotating at half of their critical velocity are likely to avoid the pair-instability supernova. The chemical composition of the rotationally enhanced winds of very low Z stars show large CNO enhancements by factors of 103 to 107, together with large excesses of 13C and 17O and moderate amounts of Na and Al. The excesses of primary N are particularly striking. When these ejecta from the rotationally enhanced winds are diluted with the supernova ejecta from the corresponding CO cores, we find [C/Fe], [N/Fe], [O/Fe] abundance ratios that are very similar to those observed in the C-rich, extremely metal-poor stars (CEMP). We show that rotating AGB stars and rotating massive stars have about the same effects on the CNO enhancements. Abundances of s-process elements and the 12C/13C ratio could help us to distinguish between contributions from AGB and massive stars. Conclusions.
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