They are an American company. Presumably all the executives live in America. Could the EU put out an arrest warrant on them and hope the US extradites them? Could the EU then refuse to allow Qualcomm to sell anything within the EU? Would this mean Apple could then not sell any iPhones in the EU?
Just curious how such a scenario could pan out..
You really don't want to do this, who knows what they will take. It could be something that is important for running the company and this could wreak a lot of havoc.
They could start by adding a daily-fine for each day they don't pay the fine; then interest on top. Then, you can imagine all smartphones with a Qualcomm chipset suddenly being banned from a 510M+ people market. All companies in Europe being barred from doing any business with Qualcomm; all Qualcomm IP nullified in Europe. Imagine having any of your officials not being able to travel inside Europe and cross-extradition countries, forever. The list goes on.
In reality, the EU is world's largest economy, with about 20% of world GDP. It is also under the "rule of law", even more than the US by some measures.
In such a society with a long history of democracy and judicial independence, it is almost by definition impossible for a company to be ruined by government action unless it commits universally-recognised crimes (fraud, corruption etc.) or its business by nature entails equally recognized negative external effect (tobacco, environmental damage,...).
Because of the undertone possibly hinting at nationalistic motives (i. e. Europe harming a foreign competitor for its own business' benefit), I'll also point out that fines by the EU have historically tracked almost perfectly with the relative size of world regions' activity in the EU. In other words: European companies make up, say, 60% of the European market, and are also hit with 60% of the total fines.
The only divergence from this correlation has actually been a slightly lower number and amount of fines against US companies, and slightly higher enforcement actions against Asian companies. I believe this is most likely caused by the US' own national enforcement (and, as a result, corporate governance) being in better shape than Asia's.
to add to this, most of the european fines don't make the news because they either consist of a "mundane" market (like a major steel fabrication plant in italy) or are simply for smaller companies which won't make international news anyways.
IANAL but I would expect EU antitrust law is a civil matter, not penal, so no, jail would be off the table. The EU has no police corps and no real "law" - it emanates resolutions that countries then turn into laws, and provides a location where treaties can be signed. Some of these laws and treaties define certain specific roles for certain EU authorities.
This is why the EU Commission will only ever emit "fines" and "sanction infractions", rather than prosecuting this or that person.
This said, the usual procedure is to perpetuate and escalate fines: they will fine you the first time, and if you keep misbehaving they will fine you pretty much every year, plus compounded interest of course. If you don't pay, they can ask specific countries to act and freeze or requisite your assets, or worse - depending on the laws of the specific country. Countries can (and occasionally do) choose to ignore these demands, but it would result in sanctions against the country, which are directly taken out of payments from the EU budget (for infrastructural work, education etc etc). This is, incidentally, why Ireland is forced to abide by the tax ruling on Apple: if they don't, EU funds will dry up until the whole sum is repaid.
In the worst-case scenario, the EU Commission could emit a directive banning all products from Qualcomm in the EU market, and let fines spiral into the trillions, but somehow I don't expect this will actually happen.