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 $(\mathcal A,\mathcal H, D)$, a compact quantum group $\mathbb G$ acting algebraically and by orientation-preserving isometries on $(\mathcal A,\mathcal H,D)$ and a unitary fiber functor $\psi$ on $\mathbb G$. The deformation procedure is a genuine generalization of the cocycle deformation of Goswami and Joardar.