  Brain-Computer Interfaces (BCIs) are a groundbreaking technology for
interacting with external devices using brain signals. Despite advancements,
electroencephalogram (EEG)-based Motor Imagery (MI) tasks face challenges like
amplitude and phase variability, and complex spatial correlations, with a need
for smaller model size and faster inference. This study introduces the LGL-BCI
framework, employing a Geometric Deep Learning Framework for EEG processing in
non-Euclidean metric spaces, particularly the Symmetric Positive Definite (SPD)
Manifold space. LGL-BCI offers robust EEG data representation and captures
spatial correlations. We propose an EEG channel selection solution via a
feature decomposition algorithm to reduce SPD matrix dimensionality, with a
lossless transformation boosting inference speed. Extensive experiments show
LGL-BCI's superior accuracy and efficiency compared to current solutions,
highlighting geometric deep learning's potential in MI-BCI applications. The
efficiency, assessed on two public EEG datasets and two real-world EEG devices,
significantly outperforms the state-of-the-art solution in accuracy ($82.54\%$
versus $62.22\%$) with fewer parameters (64.9M compared to 183.7M).
