In theory perhaps but it's a pretty damning indictment of their near term prospects so I would be surprised if they gain anything when the dust settles.

In terms of market cap, sure. But isn't part of owning a significant chunk of a company some voting power too? If the end goal of sanctions is to influence behavior then isn't it weird to give up voting power in a business in the sanctioned country?

I'm by no means knowledgeable about this stuff, so please correct me if I'm wrong.

For that voting power to exist, you’d need to be able to exercise it and/or have someone in the appropriate jurisdiction with power who would back up your claim to do so.

Realistically, that isn’t happening anytime in the foreseeable future.

I still don't get how this is a logical path. If BP wanted to hurt Rosneft wouldn't keeping the shares but announcing that they saw them as worthless except as a tool to influence russia be more impactful? Or any other path that would indicate their lack of trust in the company but still retain a way to influence it if that door opened again?

Even if BP considers the shares and the voting power completely and utterly worthless the other owners of Rosneft apparently don't and giving back the shares gives the other shareholders larger ownership of the company for free.

BP, per the article, has not decided what they will do exactly - “[…] without saying how it plans to extricate itself.”

They just don’t want to be involved anymore.

Realistically if they keep their shares, they’ll get hounded by everyone to do said influencing or whatever, which would be really irritating for them I imagine. But maybe they will put them in a drawer somewhere in the basement and tell everyone to screw off. Who knows. They say they don’t know right now.

That seems really weird. why give them a free gift? I suspect there must be more to this.

The gift is worth nothing or actually worse, BP pulling out reduces the value of all of their other shares too.

Surely (if that's really the case) just selling on the market and crashing the price would've hurt them even more. I'd normally expect that'd also make BP at least a bit of money but I have no idea about the complex accounting and tax situation when doing it this way.

Either way, at minimum it's a gift of not crashing the price.