Can you use a fetch land to search your library during your opponent's turn?

Fetch lands (such as Flooded Strand or Scalding Tarn) have activated abilities — they don't say 'Sorcery speed' or 'activate only as a sorcery,' so they follow the default timing rules for activated abilities. Under CR 116.1 and 502.1, you may activate an ability any time you have priority, including on your opponent's turn.

CR 116.1 establishes that players may cast spells or activate abilities whenever they have priority. CR 502.1 clarifies that activated abilities without a special timing restriction can be activated any time their controller could play an instant. Since instants can be played any time you have priority (CR 307.1 equivalent for abilities), fetch lands are usable at instant speed — in response to spells, during combat, end steps, etc.

This is very commonly exploited in competitive play: players often wait until the opponent's end step to activate a fetch land. This delays the land entering tapped (if relevant), and keeps mana open for instants during your turn, while still finding the correct land at a strategic moment.

Concrete example: It's your opponent's turn and they pass to their end step. You activate Misty Rainforest by paying 1 life and sacrificing it, searching your library for a Forest or Island and putting it into play tapped. This is perfectly legal — you had priority during the end step and the ability has no sorcery-speed restriction.

Note: the land found enters the battlefield tapped by default (as stated on the card itself), regardless of when you activate the fetch land.