We present a GAN Transformer framework for general action-conditioned 3D human motion generation, including not only single-person actions but also multi-person interactive actions. Our approach consists of a powerful Action-conditioned motion transFormer (ActFormer) under a GAN training scheme, equipped with a Gaussian Process latent prior. Such a design combines the strong spatio-temporal representation capacity of Transformer, superiority in generative modeling of GAN, and inherent temporal correlations from latent prior. Furthermore, ActFormer can be naturally extended to multi-person motions by alternately modeling temporal correlations and human interactions with Transformer encoders. We validate our approach by comparison with other methods on larger-scale benchmarks, including NTU RGB+D 120 and BABEL. We also introduce a new synthetic dataset of complex multi-person combat behaviors to facilitate research on multi-person motion generation. Our method demonstrates adaptability to various human motion representations and achieves leading performance over SOTA methods on both single-person and multi-person motion generation tasks, indicating a hopeful step towards a universal human motion generator.