Deformations of spectral triples and their quantum isometry groups via monoidal equivalences

In this paper, we propose a new procedure to deform spectral triples and their quantum isometry groups. The deformation data are a spectral triple ( A , H , D ) , a compact quantum group G acting algebraically and by orientation-preserving isometries on ( A , H , D ) and a unitary fiber functor ψ on G . The deformation procedure is a proper generalization of the cocycle deformation of Goswami and Joardar.