Aims. We investigate the different manifestations of AGN feedback in the evolved, powerful radio source 3C293 and their impact on the molecular gas of its host galaxy, which harbors young star-forming regions and fast outflows of HI and ionized gas. Methods. We study the distribution and kinematics of the molecular gas of 3C293 using high spatial resolution observations of the CO(1-0) and CO(2-1) lines, and the 3 and 1mm continuum taken with the IRAM PdBI. We mapped the molecular gas of 3C293

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... d compared it with the dust and star-formation images of the host. We searched for signatures of outflow motions in the CO kinematics, and reexamined the evidence of outflowing gas in the HI spectra. We also derived the star formation rate (SFR) and efficiency (SFE) of the host with all available SFR tracers from the literature, and compared them with the SFE of young and evolved radio galaxies and normal star-forming galaxies. Results. The CO(1-0) emission line shows that the molecular gas in 3C293 is distributed along a massive (2.2E10 Msun) warped disk with diameter of 21 kpc that rotates around the AGN. Our data show that the dust and the star formation are clearly associated with the CO disk. The CO(2-1) emission is located in the inner 7 kpc (diameter) region around the AGN, coincident with the inner part of the CO(1-0) disk. Both the CO(1-0) and CO(2-1) spectra reveal the presence of an absorber against the central regions of 3C293 that is associated with the disk. We do not detect any fast (>500 km/s) outflow motions in the cold molecular gas. The host of 3C293 shows an SFE consistent with the Kennicutt-Schmidt law. The apparently low SFE of evolved radio galaxies may be caused by an underestimation of the SFR and/or an overestimation of the molecular gas densities in these sources. We find no signatures of AGN feedback in the molecular gas of 3C293.