Hi,
We have explored this same question. There is some guidance (sorry I forget where) which suggest that the PRRC for the Authorised Rep needs to be based within the EU. So, essentially you can set up an EU entity and put agreements in place to make them the EU AR - as long as that entity has access to an EU based PRRC.
As to how virtual this can be is an open question. EU ARs are subject to audit so it really depends on how information is kept and how contact to that virtual office is made.