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In hybrid PET/MR systems, attenuation maps can be derived from MR to correct for attenuation in PET. However, MR-based attenuation correction (AC) in abdominal applications remains challenging (i) because of poor signal from important tissue types in common MR sequences (e.g., cortical bone) and (ii) because of respiratory motion which results in misalignments between the derived attenuation maps and the PET emissions. Furthermore, respiratory motion also leads to motion-blurring artefacts in the final PET reconstructions. In this paper, we compute an MR-based 4D attenuation map including cortical bone by combining an Ultrashort Echo Time (UTE) acquisition with a subject-specific motion model derived from a second near real-time 3D MR image acquisition. This model allows us to create attenuation maps at any respiratory position which are used for AC in the reconstruction of different respiratory resolved PET images. The inverse of the model is used for motion compensation (MC) of these images. We demonstrate our approach on MR data from 5 healthy volunteers including 3 manually inserted artificial lesions. The impact of bone tissue and respiratory motion on AC is investigated in PET simulations (i) by misclassifying bone to soft tissue in the attenuation maps leading to errors of up to 26.0% in mean uptake for lesions close to bone, and (ii) by using a non-moving attenuation map leading to errors of up to 24.2%. The impact of respiratory motion on MC showed errors of up to 50.7% in areas of strong motion if MC was not performed. The results show that the effect of motion has to be considered both for attenuation correction and for motion-compensating PET emissions. This additive effect of motion is larger than the effect of a wrong AC.