(Abridged) We present an investigation of kinematical imprints of AGN feedback on the Warm Ionized gas Medium (WIM) of massive early-type galaxies (ETGs). To this end, we take a two-fold approach that involves a comparative analysis of Halpha velocity fields in 123 local ETGs from the CALIFA integral field spectroscopy survey with 20 simulated galaxies from high-resolution hydrodynamic cosmological SPHgal simulations. The latter were re-simulated for two modeling setups, one with and another without AGN feedback. In order to quantify the effects of AGN feedback on gas kinematics we measure three parameters that probe deviations from simple regular rotation using the kinemetry package. These indicators trace the possible presence of distinct kinematic components in Fourier space (k3,5/k1), variations in the radial profile of the kinematic major axis (sigma_PA), and offsets between the stellar and gas velocity fields (Delta Phi). These quantities are monitored in the simulations from a redshift 3 to 0.2 to assess the connection between black hole accretion history, stellar mass growth and kinematical perturbation of the WIM. Observed local massive galaxies show a broad range of irregularities, indicating disturbed warm gas motions, irrespective of being classified via diagnostic lines as AGN or not. Simulations of massive galaxies with AGN feedback generally exhibit higher irregularity parameters than without AGN feedback, more consistent with observations. Besides AGN feedback, other processes like major merger events or infalling gas clouds can lead to elevated irregularity parameters, but they are typically of shorter duration. More specifically, k3,5/k1 is most sensitive to AGN feedback, whereas Delta Phi is most strongly affected by gas infall.
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