Shocking Transformation (Core 140) states:

"Action: Sacrifice one of your characters to search your deck for a non-Ancient One character and put it into play. Then, shuffle your deck."

"One of your characters" is kinda confusing. It's not "One of the characters you control" or "One of the craracters you own"

Can I use Shocking Transformation on a character I own, but controlled by my opponent by a Stygian Eye (Into Tartarus 96) or an Infernal Obsession (The Antediluvian Dreams 51)?

Technically speaking, it's still "One of my characters", even if controlled by my opponent.

Thanks for the help, and may Cthulhu eat you first.

If you have taken control of a character, it's your character. To be fair, the wording is… murky. So yes, you can definitely use Shocking Transformation on a character you've seized control of through Stygian Eye, Infernal Obsession, or any of the other Hastur cards that do this (Apeirophobia I think?).

EDIT: I just reread your post. You won't be able to sacrifice one of the characters you OWN if someone else has CONTROL of it.

You can only pay costs with cards you control. Going through CardGameDB.com it seems like a safe rule of thumb is a card should assume to refer to controller unless otherwise specified.

Got it, thanks. It was a question made after the last Italian Regionals, after a very ill-timed shocking transformation

I wanted to be sure ^^

Anyway, unless specified otherwise on the card, "your X" only refers to "X" you control and not "X" you own. That's somewhere in the rulebook or the FAQ.

I send a mail to Damon some time ago:

QUESTION:

I play Revelation of the Spheres. It says: Reveal the top 5 cards of an opponent's deck. Put into play a character revealed this way under your control.

I now want to trigger Stalking Hound "After an opponent's character enters play due to a triggered effect…" Can I?

Does the Hound look at ownership or control?

ANSWER:

It looks at the controller. Most effects look to the controller unless owner is spelled out. Usually when an opponent's character is entering play the controller and owner are the same thing but obviously there are cases were this is not the case.