Under certain curcumstances you can loose your Green Card
Dear 123mri,
you can stay abroad for up to one year without a re-entry permit. If you work abroad, you have to file your taxes in USA, too, because you have to declare your worldwide income.
It sounds as if your job offer is of permanent nature. That means, you are considering of staying in Europe permanently. As a Green Card holder you are a permanent resident of the US. So if someone notices that you have lived and worked abroad your Green Card will be revoked.
In your situation you have to choose whether you want an interesting job in Europe or whether you want to keep your Green Card. You can't get both.
Sincerely,
Haary