Europe: big fly with black/yellow striped body: I'm guessing a horse fly?
At first, because of the size and shape, I thought that it was a horsefly, but no horsefly looks like that (at least not in Luxembourg). It turns out that it was a hoverfly, just as Karl Kjer said. The species is Volucella zonaria, or the hornet mimic hoverfly. This hoverfly lives in most of Europe (including Luxembourg) and is 15-25 mm in length, consistent with your 20 mm estimate.

In this image you can see the same coloration and abdominal markings as your insect.



The markings in your photo are very difficult to see but are there.





Wikipedia page

original image source