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Generative Information Retrieval is an emerging retrieval paradigm that exhibits remarkable performance in monolingual scenarios. However, applying these methods to multilingual retrieval still encounters two primary challenges, cross-lingual identifier misalignment and identifier inflation. To address these limitations, we propose Multilingual Generative Retrieval via Cross-lingual Semantic Compression (MGR-CSC), a novel framework that unifies semantically equivalent multilingual keywords into shared atoms to align semantics and compresses the identifier space, and we propose a dynamic multi-step constrained decoding strategy during retrieval. MGR-CSC improves cross-lingual alignment by assigning consistent identifiers and enhances decoding efficiency by reducing redundancy. Experiments demonstrate that MGR-CSC achieves outstanding retrieval accuracy, improving by 6.83% on mMarco100k and 4.77% on mNQ320k, while reducing document identifiers length by 74.51% and 78.2%, respectively. We publicly release our dataset and code at https://github.com/simengggg/MGR-CSC