Austrian warrant, presence in the EU: keep the surrender procedure in the state of residence in view.
If Austria issues a European Arrest Warrant and you are in another member state, the state of residence first decides on surrender. The procedure follows the Framework Decision on the European Arrest Warrant (2002/584/JHA) as transposed there. Surrender follows the principle of mutual recognition of judicial decisions.
From a legal perspective it is important to coordinate the proceedings in both states: the surrender procedure in the state of residence and the underlying criminal proceedings in Austria. Both strands interact and should be aligned early.