<p>Point cloud registration is a core task in 3D computer vision, aiming to align two point clouds by estimating rigid transformations (rotation and translation). However, existing methods still face challenges in dealing with rotation sensitivity, local feature ambiguity, and mismatches in symmetric regions. This paper presents a novel Hybrid Geometric Feature Transformer (HGFT) that integrates equivariant geometric features with global rotation-invariant features, achieving high-precision and robust point cloud registration. Specifically, HGFT consists of three core modules: 1) an Equivariant Center Point Geometric Attention Mechanism (CGAM), which leverages neighborhood geometric triplets and positional embeddings to extract rotation-sensitive local features; 2) a Geometric Gated Dynamic Fusion Mechanism (GGDF), which adaptively fuses local equivariant features with global Point Pair Features (PPF) rotation-invariant features; and 3) a Symmetry-Aware Attention Mechanism (SAGA), which suppresses mismatches by dynamically penalizing attention weights in symmetric regions. Additionally, a Maximum Clique Transformation Evaluator (MTE) is proposed, which uses geometric consistency constraints to filter high-confidence point correspondences, further enhancing the robustness of transformation estimation. Experimental results indicate that HGFT significantly outperforms existing methods on multiple public datasets, demonstrating particularly strong generalization under noisy conditions, partial overlap, and highly symmetric scenes. It achieves Registration Recall (RR) scores of 95.2% and 78.3% on the 3DMatch and 3DLoMatch benchmarks, respectively.</p>