In domain adaptation (DA), the effectiveness of deep learning-based models is often constrained by batch learning strategies that fail to fully apprehend the global statistical and geometric characteristics of data distributions. Addressing this gap, we introduce 'Global Awareness Enhanced Domain Adaptation' (GAN-DA), a novel approach that transcends traditional batch-based limitations. GAN-DA integrates a unique predefined feature representation (PFR) to facilitate the alignment of cross-domain distributions, thereby achieving a comprehensive global statistical awareness. This representation is innovatively expanded to encompass orthogonal and common feature aspects, which enhances the unification of global manifold structures and refines decision boundaries for more effective DA. Our extensive experiments, encompassing 27 diverse cross-domain image classification tasks, demonstrate GAN-DA's remarkable superiority, outperforming 24 established DA methods by a significant margin. Furthermore, our in-depth analyses shed light on the decision-making processes, revealing insights into the adaptability and efficiency of GAN-DA. This approach not only addresses the limitations of existing DA methodologies but also sets a new benchmark in the realm of domain adaptation, offering broad implications for future research and applications in this field.