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Robotics has long been a field riddled with complex systems architectures whose modules and connections, whether traditional or learning-based, require significant human expertise and prior knowledge. Inspired by large pre-trained language models, this work introduces a paradigm for pre-training a general purpose representation that can serve as a starting point for multiple tasks on a given robot. We present the Perception-Action Causal Transformer (PACT), a generative transformer-based architecture that aims to build representations directly from robot data in a self-supervised fashion. Through autoregressive prediction of states and actions over time, our model implicitly encodes dynamics and behaviors for a particular robot. Our experimental evaluation focuses on the domain of mobile agents, where we show that this robot-specific representation can function as a single starting point to achieve distinct tasks such as safe navigation, localization and mapping. We evaluate two form factors: a wheeled robot that uses a LiDAR sensor as perception input (MuSHR), and a simulated agent that uses first-person RGB images (Habitat). We show that finetuning small task-specific networks on top of the larger pretrained model results in significantly better performance compared to training a single model from scratch for all tasks simultaneously, and comparable performance to training a separate large model for each task independently. By sharing a common good-quality representation across tasks we can lower overall model capacity and speed up the real-time deployment of such systems.