Learn Icelandic: Þau umbuna sjálfum sér alltaf eftir vinnuna. - They always reward themselves after work.

The verb umbuna (to reward) requires its object to be in the dative case. The reflexive pronoun for 'themselves' is sér. To add emphasis, we include the intensifying pronoun sjálfur, which must agree with the neuter plural subject Þau and take the dative case, resulting in sjálfum.

Could we just say Þau umbuna sér without sjálfum?

Yes, Þau umbuna sér is grammatically correct and means 'They reward themselves.' Adding sjálfum simply emphasizes that they are rewarding themselves specifically, rather than someone else.

Why is vinnuna in the accusative case? Doesn't the preposition eftir usually take the dative?

This is a great rule to remember: eftir takes the accusative case when it refers to time, meaning 'after' (like 'after the work' here). It takes the dative case when referring to physical space, such as 'following' or 'along' something.

Why does the adverb alltaf come after sjálfum sér instead of before the verb like in English?

In Icelandic main clauses, adverbs of frequency like alltaf (always) typically come after the verb and its object or reflexive pronoun, rather than squeezing between the subject and the verb.