We propose a new approach to Physical Telepresence, based on shared workspaces with the ability to capture and remotely render the shapes of people and objects. In this paper, we describe the concept of shape transmission, and propose interaction techniques to manipulate remote physical objects and physical renderings of shared digital content. We investigate how the representation of user's body parts can be altered to amplify their capabilities for teleoperation. We also describe the details of building and testing prototype Physical Telepresence workspaces based on shape displays. A preliminary evaluation shows how users are able to manipulate remote objects, and we report on our observations of several different manipulation techniques that highlight the expressive nature of our system.