The paper introduces the Lorentz Geometric Algebra Transformer (L-GATr), a novel architecture designed for high-energy physics applications. L-GATr represents high-energy data using geometric algebra over four-dimensional space-time and is equivariant under Lorentz transformations, which are the symmetry group of relativistic kinematics. The architecture is also a Transformer, making it versatile and scalable for large systems. L-GATr is first demonstrated on regression and classification tasks from particle physics, and then used to construct the first Lorentz-equivariant generative model based on a continuous normalizing flow. Across various experiments, L-GATr shows performance on par with or better than strong domain-specific baselines. The architecture is particularly effective in handling the high-dimensional and complex distributions common in particle physics data, and it scales well to large datasets. The implementation of L-GATr is available at \url{https://github.com/heidelberg-hepm/lorentz-gatr}.The paper introduces the Lorentz Geometric Algebra Transformer (L-GATr), a novel architecture designed for high-energy physics applications. L-GATr represents high-energy data using geometric algebra over four-dimensional space-time and is equivariant under Lorentz transformations, which are the symmetry group of relativistic kinematics. The architecture is also a Transformer, making it versatile and scalable for large systems. L-GATr is first demonstrated on regression and classification tasks from particle physics, and then used to construct the first Lorentz-equivariant generative model based on a continuous normalizing flow. Across various experiments, L-GATr shows performance on par with or better than strong domain-specific baselines. The architecture is particularly effective in handling the high-dimensional and complex distributions common in particle physics data, and it scales well to large datasets. The implementation of L-GATr is available at \url{https://github.com/heidelberg-hepm/lorentz-gatr}.