  We study an interacting $\lambda\,\phi^4_{\star}$ scalar field defined on
Snyder-de Sitter space. Due to the noncommutativity as well as the curvature of
this space, the renormalization of the two-point function differs from the
commutative case. In particular, we show that the theory in the limit of small
curvature and noncommutativity is described by a model similar to the
Grosse-Wulkenhaar one. Moreover, very much akin to what happens in the
Grosse-Wulkenhaar model, our computation demonstrates that there exists a fixed
point in the renormalization group flow of the harmonic and mass terms.
