Please see Article 11 , Article 12 , Article 15 , Article 31 of the EU MDR.
The AR is an economic operator and will have all the obligations in the EU as much as the manufacturer.
At almost all places the EU MDR mentions "Manufacturer or its Authorised Representative"
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(35) For manufacturers who are not established in the Union, the authorised representative plays a pivotal role in ensuring the compliance of the devices produced by those manufacturers and in serving as their contact person established in the Union. Given that pivotal role, for the purposes of enforcement it is appropriate to make the authorised representative legally liable for defective devices in the event that a manufacturer established outside the Union has not complied with its general obligations. The liability of the authorised representative provided for in this Regulation is without prejudice to the provisions of Directive 85/374/EEC, and accordingly the authorised representative should be jointly and severally liable with the importer and the manufacturer. The tasks of an authorised representative should be defined in a written mandate. Considering the role of authorised representatives, the minimum requirements they should meet should be clearly defined, including the requirement of having available a person who fulfils minimum conditions of qualification which should be similar to those for a manufacturer's person responsible for regulatory compliance.