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Infrastructure-to-vehicle (I2V) group message delivery is a common operation required by a wide variety of vehicular ad hoc network (VANET) applications. However, due to the highly dynamic mobility in VANETs, it remains a difficult problem to deliver messages to a group of moving vehicles scattering over the whole network. The contribution of this paper is to propose the first trajectory-based I2V group message delivery protocol, TGMD, that exploits vehicle trajectories to improve the group-message delivery performance. TGMD contains two phases. The first phase determines a few rendezvous points from which the member vehicles can receive the message. Then the second phase transmits the group message over multiple hops to these selected rendezvous points using a multicast-like forwarding scheme to avoid redundant packet transmissions over the overlapped road segments. TGMD aims to minimize the required number of network-layer packet transmissions under a relatively loose delay constraint. Our extensive simulation results indicate that in comparison with the trajectory-based single-destination I2V message delivery scheme (through N-unicasting), TGMD significantly reduces the required number of packet transmissions (and thus bandwidth consumption) while achieving a high delivery ratio around 90%.