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While there is overwhelming observational evidence of AGN-driven jets ingalaxy clusters and groups, if and how the jet energy is delivered to theambient medium remains unanswered. Here we perform very high resolution AGN jetsimulations within a live, cosmologically evolved cluster with the moving meshcode AREPO. We find that mock X-ray and radio lobe properties are in goodagreement with observations with different power jets transitioning from FR-Ito FR-II-like morphologies. During the lobe inflation phase, heating by bothinternal and bow shocks contributes to lobe energetics, and $\sim 40$ per centof the feedback energy goes into the $PdV$ work done by the expanding lobes.Low power jets are more likely to simply displace gas during lobe inflation,but higher power jets become more effective at driving shocks and heating theintracluster medium (ICM), although shocks rarely exceed $\mathcal{M}\sim 2-3$.Once the lobe inflation phase ceases, cluster weather significantly impacts thelobe evolution. Lower power jet lobes are more readily disrupted and mixed withthe ICM, depositing up to $\sim 70$ per cent of the injected energy, however,ultimately the equivalent of $\gtrsim 50$ per cent of the feedback energy endsup as potential energy of the system. Even though the mean ICM entropy isincreased up to $80$~Myr after the jets switch off, AGN heating is gentle,inducing no large variations in cluster radial profiles in accord withobservations.

AGN jet feedback on a moving mesh: gentle cluster heating by weak shocks and lobe disruption