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In bilateral teleoperation, a human operator manipulates a remote environment through a pair of master and slave robots. The transparency quantifies the fidelity of the teleoperation system, and is typically defined as the ability to accurately display remote environment properties to the operator. We propose a novel multidimensional measure of transparency which takes into account the human operator and consists of three components: 1) perceptual transparency, which quantifies human perception of the remote environment, 2) local motor transparency, which quantifies how far is the movement of the human operator from ideal, and 3) remote motor transparency, which describes how far is the movement of the remote device from ideal. We suggest that for many practical applications, the goal of the transparency optimization is to maintain perceptual and remote motor transparency while sacrificing local motor transparency, and that it is plausible to take advantage of the gap between perception and action in the operators sensorimotor system. We prove analytically that for a teleoperation channel with a position and force scaling and a constant transmission delay, in a palpation and perception of stiffness task, it is possible to find gains that ensure perfect perceptual and remote motor transparency while maintaining stability. We also show that stability depends on the operator that maintain sufficient arm impedance relative to environment impedance and delay.