You can't fix it. If you consider yourself obese then either go to eBay or Amazon and purchase a new metal star base. Measure the length between wheels that are close to 180 degrees apart.
So for example:
How tall are you and do you also have problems with the gas cylinder?
Yep, it's going to need to be a mechanical solution. I seriously doubt any adhesive is going to work.
If you can find a exhaust clamp that fits, that would probably work.
Or, measure the size of the hole (or what it should be on an undamaged chair), and grab a replacement base. It probably won't match 100%, but still better than replacing the whole chair.
Unfortunately, these sellers don't ship to spain.
Do you think something like this would work? https://www.amazon.com/Heavy-Duty-Replacement-Office-Chair/dp/B00CDPZTWO/ref=sr\_1\_30?crid=3KP647STEA5BW&keywords=aeron+aluminum+base&qid=1644183689&sprefix=aeron+aluminum+base%2Caps%2C144&sr=8-30
I bought some replacement caster wheels for my office chair on Amazon a few weeks ago. They were MUCH cheaper than any local shop. One of the suggested link "others bought" links looks like that broken part.
Staples Dexley, got it for $150 on sale. It goes on sale pretty frequency around that price, and if you set up a deal alert on slickdeals, you'll know when it goes on sale. I really like it because the seat is wide so you can sit cross legged which is issue for even most high-end chairs like the Aeron and it comes with a pretty nice height adjustable headrest. The one thing I don't like about the chair is the plastic base (plastic so it cracks if you jump into your chair a lot), gas pump (doesn't go that high up), and wheels (don't roll too well on carpet). I upgraded those parts and now the chair is epic, I used these parts for the new base, gas pump, and wheels. All in I'm about $260 which is waaaay less than a used Aeron which is around $350-400 on Facebook marketplace. Even without the upgrades, it still a great chair, and if your base does crack (like it did mine), you have a 7-year warranty on the chair so you can either get a replacement part or a brand new chair if they don't have the individual part (happened to me).
Also, will this star work? https://www.amazon.com/dp/B00CDPZTWO/ref=dp_prsubs_2