This paper describes a system called GENTORO that uses a robot and a handheld projector for supporting children's storytelling activities. GENTORO differs from many existing systems in that children can make a robot play their own story in a physical space augmented by mixed-reality technologies. Pilot studies have been conducted to clarify the design requirements of GENTORO from both technological and practical viewpoints. A user study indicates that GENTORO's ability to enable manipulation of a robot using a handheld projector in a physical space can enhance children's embodied participation in, and their level of engagement with, their storytelling activities, and can support children in designing and expressing creative and original stories. (Contains 2 tables and 10 figures.)