Chiral crossover effects on the shear viscosity of a pion gas

The properties of strongly interacting matter are probed in ultra-relativistic heavy-ion collisions. In the context of measurements of the elliptic flow at RHIC and the LHC the shear viscosity is of particular interest. In this presentation we discuss recent results for η/s in hadronic matter at vanishing baryo-chemical potential within kinetic theory. Using the Nambu Jona-Lasinio model, special attention is paid to effects arising from the restoration of spontaneously broken chiral symmetry with increasing temperature.