BEagle,
This post is below your usual high standard.
German law is the applicable one and it doesn't provide for execution, I'm pleased to say. Nor for extradition to a country in which no offence has taken place. Nor for extradition to any country in which the extraditee may be subject to the death penalty - multiple treaty commitments provide for this, even before European human rights legislation.
Even the US usually tries and convicts people before executing them.