Ok, I'm pretty new to CoCLCG. I am trying to understand the intricasies of costs on actions.

It is clear from the rules that "sacrifice" only applies to cards you control, and destroy can apply to cards both you or your opponent control.

What about "exhaust"?

I do not see any terminology requiring or suggesting that you must choose a character that you control to exhaust it (except in cases where is specified "you control" of course).

So, if a card says:

Action: Exhaust a character to do "X"

I see nothing in the rules or FAQ that prevents me from exhausting one of my opponent's characters.

Yes, a lot of cards say to exhaust that specific card, or exhaust a card that you control. But, some do not.

For example:

Deep One Scouts - "Exhaust 2 Deep One characters to … "

If my opponent had Deep One characters in play, could I exhaust his Deep Ones to trigger the effect? I see nothing to prevent it.

Flanking Maneuver - "Exhaust two characters, each with at least [C], to choose and destroy…"

It does not specify whose characters to exhaust. Can you exhaust your opponent's characters to trigger this card? So, I could exhaust two of my opponent's characters as well as destroying a third (the effect)?

It makes logical sense, as far as card text goes. Especially since the majority of cards do specify the card to exhaust or the card controller. On the other hand it does seem awful and odd to do either of the examples above to my opponent's characters.

I had same thoughts as you when I started playing. Important part is FAQ which says everything said before "to" is part of the cost of the card or triggered effect.

So "Exhaust 2 Deep One characters to…" and "Exhaust two characters, each with at least [C], to…" is part of the cost. You can only pay cost with cards you control so you can't exhaust opponents characters as part of the cost.

Aha, thanks for that! Makes better sense now.