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We present a robust cooperative perception framework with V2X communication using a novel vision Transformer. Specifically, we build a holistic attention model, namely V2X-ViT, to effectively fuse information across on-road agents (i.e., vehicles and infrastructure). V2X-ViT consists of alternating layers of heterogeneous multi-agent self-attention and multi-scale window self-attention, which captures inter-agent interaction and per-agent spatial relationships. These key modules are designed in a unified Transformer architecture to handle common V2X challenges, including asynchronous information sharing, pose errors, and heterogeneity of V2X components. To validate our approach, we create a large-scale V2X perception dataset using CARLA and OpenCDA. Extensive experimental results demonstrate that V2X-ViT sets new state-of-the-art performance for 3D object detection and achieves robust performance even under harsh, noisy environments. 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