Vladimir wrote:
I have friends with green cards and it’s a real pain if you are not planing to live in the US: you have to pay taxes, explain why you are not there all the time
If you are inside the US for less than 31 days per calendar year you not a tax resident. If you are inside the US more than 31 days/year then as a US Permanent Resident, which is what a Green Card means, you have to file an income tax return. Assuming you’re paying taxes on your income in another country you will be unlikely to pay US income taxes.
You do have some explaining to do if you want to maintain US Permanent Resident status without actually living in the country 
The official rule is that you cannot be absent from the US for more than a year, but if USCIS gets the idea your purpose in visiting is only to maintain status, but that you aren’t actually a resident, their intent will be to remove your status.
Vladimir wrote:
Also in Europe you are almost forbidden to have bank accounts or trade shares if you have a green card.
It’s difficult for me to imagine how anybody in Europe would know your US immigration status? I would never discuss US immigration status with any non-US entity.
I did have a situation once in which an immediate family member living in Germany was asked to produce documentation on my US income (i.e. total family income). The solution was for that family member to say they didn’t know, that I’m not a German citizen and that I refused to provide the data. That worked fine 
172driver wrote:
All that said, there is another option which some people do: buy a small plane in the US and lease it back to a flight school. Then come over when you like and go flying. AFAIK this is usually done through a company setup, but doesn’t have to be very expensive. With luck, the plane pays for itself
That’s a neat idea!
“I would never discuss US immigration status with non-US entities”.
And what do you use to open an account? Your pilot licence or your blue passport?
Silvaire wrote:
You do have some explaining to do if you want to maintain US Permanent Resident status without actually living in the country
If I only want to fly for 3-6 months, I will have to do the explaining. And then give up the green card. With more explaining. And that all only after I succeed to get it. It’s an option but it’s a difficult one.
Silvaire wrote:
It’s difficult for me to imagine how anybody in Europe would know your US immigration status?
Since the US did all that stuff with the Swiss banks, you have to sign every time you do something in a bank that you are not a US citizen, don’t hold a green card or a temporary or permanent residency permit of any kind or you have any other permanent connections with the US. If you lie you are liable under a bunch of criminal laws. And if you say “yes” then the bank says “thanks but no thanks, we don’t want your business”. I’ve seen that first hand when helping a new colleague from the US who came to work in Switzerland and actually left only 3 months later.
