Abstract: Given a spectral triple $(A,H,D)$ and a $C^*$-dynamical system $(\bA, G, \alpha)$ where $A$ is dense in $\bA$ and $G$ is a locally compact group, we extend the triple to a triplet $(\algA,\caH,\DD)$ on the crossed product $G \ltimes_{\alpha, \red} \bA$ which can be promoted to a modular-type twisted spectral triple within a general procedure exemplified by two cases: the $C^*$-algebra of the affine group and the conformal group acting on a complete Riemannian spin manifold.