Hi,
This is straight off the WikiPedia page:
Object Push Profile (OPP)
A basic profile for sending "objects" such as pictures, virtual business cards, or appointment details. It is called push because the transfers are always instigated by the sender (client), not the receiver (server).
OPP uses the APIs of OBEX profile and the OBEX operations which are used in OPP are connect, disconnect, put, get and abort. By using these API the OPP layer will reside over OBEX and hence follow the specifications of the Bluetooth stack.
And from my understanding just because it is a Push profile does not mean GET is not supported.
Is the GET something you can add to the OPPServer?