Azimuthal asymmetries in $p^\uparrow p \to {\rm jet}\, \pi\, X$

We study the azimuthal asymmetries for the distributions of leading pions inside a jet produced inclusively in high-energy proton-proton collisions within the framework of the transverse momentum dependent generalized parton model. We present results for the RHIC center-of-mass energies $\sqrt{s}$ = 200 and 500 GeV, mainly for forward jet rapidities, in particular for the two mechanisms which dominate such asymmetries: the Sivers and the Collins effects. We also briefly discuss the case of inclusive jet production and, adopting the so-called colour gauge invariant parton model, we propose a phenomenological analysis of the process dependence of the quark Sivers function.