Breakdown of Wir kennen den Schauspieler, dessen Film sie gestern zeigten.
wir
we
sie
they
kennen
to know (somebody/something)
der Film
the movie / the film
Questions & Answers about Wir kennen den Schauspieler, dessen Film sie gestern zeigten.
Why do we use dessen here instead of deren?
dessen is the Genitive relative pronoun for masculine and neuter nouns. Here, it refers back to the masculine noun der Schauspieler (the actor). If the sentence were about a female actress (die Schauspielerin), you would use the feminine form deren instead.
Wait, Film is the direct object being shown. Why doesn't dessen get an Accusative ending like seinen would?
That is the beauty of dessen and deren! Unlike normal possessive words (like mein or sein), which change their endings to match the noun they are attached to, dessen and deren are completely frozen. They tell you the gender of the owner (the actor), but they never take extra endings to match the case of the object (the film).
How do we know sie means 'they' and not 'she' in this relative clause?
You have to look at the verb. The verb zeigten ends in -en, which is the plural form ('they showed'). If the sentence meant 'whose film she showed', the verb would be singular: zeigte.
Why is zeigten pushed to the very end of the sentence?