  In the context of non-commutative geometries, we develop a group Fourier
transform for the Lie group SU(2). Our method is based on the Schwinger
representation of the Lie algebra su(2) in terms of spinors. It allows us to
prove that the non-commutative R^3 space dual to the SU(2) group is in fact of
the Moyal-type and endowed with the Voros star-product when expressed in the
spinor variables. Finally, from the perspective of quantum gravity, we discuss
the application of these new tools to group field theories for spinfoam models
and their interpretation as non-commutative field theories with
quantum-deformed symmetries.
