  We formulate a quantum group analogue of the group of orinetation-preserving
Riemannian isometries of a compact Riemannian spin manifold, more generally, of
a (possibly $R$-twisted in the sense of a paper of one of the authors, and of
compact type) spectral triple. The main advantage of this formulation, which is
directly in terms of the Dirac operator, is that it does not need the existence
of any `good ' Laplacian as in our previous works on quantum isometry groups.
Several interesting examples, including those coming from Rieffel-type
deformation as well as the equivariant spectral triples on $SU_\mu(2)$ and
$S^2_{\mu 0}$ are dicussed.
