Shared autonomous vehicles (SAVs) have the potential to transform the transportation industry by combining the benefits of the shared economy and autonomous mobility. However, the successful implementation of SAVs is contingent upon public acceptance of this new technology. Previous surveys suggest that people are more interested in private autonomous vehicles than SAVs. To address this challenge, we explore the role of psychological ownership in shaping people's intention to use SAVs, and its impact on other psychological factors such as trust, perceived usefulness, and perceived risk. Psychological ownership -- the feeling of possession and control over an object or idea -- can arise even in the absence of legal ownership. In an ITS context, increasing a person's sense of psychological ownership of a SAV is envisioned to involve technological advancements in the form of a passenger's preferred temperature, seat recline angle and music choice (for example) autonomously being set prior to the SAV's arrival to collect the passenger from their origin; and a speaking avatar in the car that greets them personally, and is of service to the passenger throughout their trip. To examine our hypothesis of whether psychological ownership shapes people's intentions to use SAVs, an online questionnaire was conducted which provided one of two scenarios to participants at random: a story intended to invoke a sense of heightened psychological ownership versus a control scenario. We will present our preliminary findings and shed light on the potential effects of psychological ownership on the acceptance and usage of SAVs.