Actually they can - the second you place your foot on EU (or collaborating - extradition treaties) soil, and of course if you want to do business in EU then you need to have legal presence in the EU.
Extradition treaties are usually subject to 'dual criminality' - so you would have to be breaking the country you are in as well to be extradited for violation of that same law to the EU.
And be realistic. The US hasn't even successfully managed to extradite Kim Dotcom from mighty New Zealand.