  Given a free action of a compact Lie group $G$ on a unital C*-algebra
$\mathcal{A}$ and a spectral triple on the corresponding fixed point algebra
$\mathcal{A}^G$, we present a systematic and in-depth construction of a
spectral triple on $\mathcal{A}$ that is build upon the geometry of
$\mathcal{A}^G$ and $G$. We compare our construction with a selection of
established examples.
