Reinforcement Learning with Verifiable Rewards (RLVR), often optimized with Group Relative Policy Optimization (GRPO), has become a central recipe for improving the reasoning capabilities of pretrained language models but current studies remain heavily English-centric. We conduct a large-scale empirical study of multilingual and non-English GRPO across a wide range of base models, training languages, and different reasoning language rewards. We find that training to reason in the native language often leaves only a small gap to training for English reasoning. We further observe strong crosslingual transfer: training in one language often improves performance in many others. However, specific trends are highly model- and language-dependent. In some cases, training in a particular language induces severe regressions on out-of-domain capabilities in other languages. Our analysis shows that RLVR beyond English can provide broad crosslingual gains, but also requires broad evaluation to detect language-specific regressions.

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