Is it possible to be injected with something containing such a transmitter?
VeriChips, human-implantable microchips, are tiny low-frequency (LF) chips encased in glass that can be inserted under the skin using a large needle (see VeriChip Markets Its Implantable RFID Tags and Services Direct to Consumers). VeriChip was the first company to offer implantation as a service, but that firm was acquired and became known as PositiveID Corp. It has been reported that PositiveID discontinued implantation services for humans in 2010.
To answer your question, the smallest GPS transmitter that I have seen is bigger than a USB flash drive. Injecting such a device under your skin would be quite a painful procedure, leaving a very large and obvious bump on your arm. GPS devices also require a battery, so if you were to have this thing injected, you would then need to have it surgically removed every few years in order to replace the battery. Moreover, the VeriChip transponder has a read range of less than 1 foot, and is designed for short-range identification, not long-range tracking.
—Mark Roberti, Founder and Editor, RFID Journal