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Graph Neural Networks (GNNs) have been shown as promising solutions for collaborative filtering (CF) with the modeling of user-item interaction graphs. The key idea of existing GNN-based recommender systems is to recursively perform the message passing along the user-item interaction edge for refining the encoded embeddings. Despite their effectiveness, however, most of the current recommendation models rely on sufficient and high-quality training data, such that the learned representations can well capture accurate user preference. User behavior data in many practical recommendation scenarios is often noisy and exhibits skewed distribution, which may result in suboptimal representation performance in GNN-based models. In this paper, we propose SHT, a novel Self-Supervised Hypergraph Transformer framework (SHT) which augments user representations by exploring the global collaborative relationships in an explicit way. Specifically, we first empower the graph neural CF paradigm to maintain global collaborative effects among users and items with a hypergraph transformer network. With the distilled global context, a cross-view generative self-supervised learning component is proposed for data augmentation over the user-item interaction graph, so as to enhance the robustness of recommender systems. Extensive experiments demonstrate that SHT can significantly improve the performance over various state-of-the-art baselines. Further ablation studies show the superior representation ability of our SHT recommendation framework in alleviating the data sparsity and noise issues. The source code and evaluation datasets are available at: https://github.com/akaxlh/SHT.