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This paper presents novel hybrid architectures that combine grid- and point-based processing to improve the detection performance and orientation estimation of radar-based object detection networks. Purely grid-based detection models operate on a bird's-eye-view (BEV) projection of the input point cloud. These approaches suffer from a loss of detailed information through the discrete grid resolution. This applies in particular to radar object detection, where relatively coarse grid resolutions are commonly used to account for the sparsity of radar point clouds. In contrast, point-based models are not affected by this problem as they process point clouds without discretization. However, they generally exhibit worse detection performances than grid-based methods. We show that a point-based model can extract neighborhood features, leveraging the exact relative positions of points, before grid rendering. This has significant benefits for a subsequent grid-based convolutional detection backbone. In experiments on the public nuScenes dataset our hybrid architecture achieves improvements in terms of detection performance (19.7% higher mAP for car class than next-best radar-only submission) and orientation estimates (11.5% relative orientation improvement) over networks from previous literature.