Learn Finnish: Luulin uuden käänteen lunastavan kaikki odotukseni. - I thought the new twist would fulfill all my expectations.

This uses the participial construction (referatiivinen lauseenvastike), which is a more compact way to say Luulin, että uusi käänne lunastaa kaikki odotukseni. The subject of the embedded clause (uusi käänne) is put into the genitive case (uuden käänteen), and the verb becomes the present active participle (lunastavan).

Doesn't lunastaa usually mean "to redeem"?

Yes, its literal meaning is to redeem a coupon, cash a check, or claim a package. However, the set phrase lunastaa odotukset is the idiomatic and standard way to say "to fulfill expectations" or "to live up to expectations" in Finnish.

What case is odotukseni in? I don't see a plural marker for "expectations".

It is in the nominative plural, functioning as a total object. The basic plural word is odotukset, but when you attach a possessive suffix like -ni (my) to a nominative plural, the plural -t marker disappears. We can still tell it is plural because of the preceding plural modifier kaikki.

If I wanted to say "I didn't think the new twist would fulfill my expectations after all", how would I add kuitenkaan?