Vision-language-action policies learn manipulation skills across tasks, environments and embodiments through large-scale pre-training. However, their ability to generalize to novel robot configurations remains limited. Most approaches emphasize model size, dataset scale and diversity while paying less attention to the design of action spaces. This leads to the configuration generalization problem, which requires costly adaptation. We address this challenge by formulating cross-embodiment pre-training as designing policies equivariant to embodiment configuration transformations. Building on this principle, we propose a framework that (i) establishes a embodiment equivariance theory for action space and policy design, (ii) introduces an action decoder that enforces configuration equivariance, and (iii) incorporates a geometry-aware network architecture to enhance embodiment-agnostic spatial reasoning. Extensive experiments in both simulation and real-world settings demonstrate that our approach improves pre-training effectiveness and enables efficient fine-tuning on novel robot embodiments. Our code is available at https://github.com/hhcaz/e2vla