  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.
