Suspensions of multiarm star polymers are studied as models for soft colloidal glasses. Using an established pre-shearing protocol which ensures a reproducible initial state (the "rejuvenation" of the system), we report here the time evolution of the stress upon startup of simple shear flow for a range of shear rates. We show the existence of critical shear rates, gamma center dot(c)(c) which are functions of the concentration, c. When the suspensions are sheared at rates below gamma center dot(c)(c), the stress rises to a common value sigma(c)(c) which is also a function of the concentration. The system thus develops a yield stress. This behavior manifests itself as an evolution from a monotonic slightly shear-thinning flow curve to a flow curve dominated by a stress plateau. We relate this bulk evolution to spatially resolved velocity profiles. Hence, yield stress is linked to shear banding in this class of soft colloids.