Multiview detection incorporates multiple camera views to deal with occlusions, and its central problem is multiview aggregation. Given feature map projections from multiple views onto a common ground plane, the state-of-the-art method addresses this problem via convolution, which applies the same calculation regardless of object locations. However, such translation-invariant behaviors might not be the best choice, as object features undergo various projection distortions according to their positions and cameras. In this paper, we propose a novel multiview detector, MVDeTr, that adopts a newly introduced shadow transformer to aggregate multiview information. Unlike convolutions, shadow transformer attends differently at different positions and cameras to deal with various shadow-like distortions. We propose an effective training scheme that includes a new view-coherent data augmentation method, which applies random augmentations while maintaining multiview consistency. On two multiview detection benchmarks, we report new state-of-the-art accuracy with the proposed system. Code is available at https://github.com/hou-yz/MVDeTr.