Supportern hejar på hemmalaget.

The -n is the definite article attached to the noun.

• en supporter = a supporter
• supportern = the supporter

In Swedish, the definite article is usually added to the end of the noun instead of being a separate word like the in English.

Because heja på is the normal expression for to cheer for / support a team or person.

• heja by itself can mean something like cheer or shout encouragement
• heja på någon/något means cheer for someone/something

So in this sentence, på is not optional. It is part of the expression.

Here, på does not literally mean on in the physical sense. In heja på, it is just the preposition that belongs with the verb.

This is very common in Swedish, just like English has combinations such as listen to, look at, or wait for. You usually have to learn the whole phrase together:

• heja på ett lag = cheer for a team
• heja på någon = cheer for someone

Because Swedish often forms compound nouns as a single word.

Here:

• hemma = at home
• lag = team
• hemmalag = home team
• hemmalaget = the home team

English usually writes this as two words, but Swedish normally joins the parts into one word.

That -et is the definite ending for a neuter noun.

• ett lag = a team
• laget = the team

In the compound noun, the main word is lag, so the whole compound follows the same pattern:

• ett hemmalag = a home team
• hemmalaget = the home team

You know it from its indefinite form: ett lag.

In Swedish, nouns are usually either:

• en-words (common gender)
• ett-words (neuter)

Since lag is an ett-word, its definite form becomes laget, and in the compound you get hemmalaget.

No, this is normal Swedish main-clause word order:

Supportern + hejar + på hemmalaget

That is:

• subject: Supportern
• verb: hejar
• prepositional phrase/object-like complement: på hemmalaget

Swedish main clauses follow the verb-second rule, and this sentence fits that pattern perfectly because the subject comes first and the verb comes second.

Yes. In Swedish, supporter very commonly means a sports supporter or fan.

So supportern here is naturally understood as the supporter / the fan, especially in a sports context.

It means the home team in the sports sense: the team playing on its own ground or in its own arena.

So it is not just any team that happens to be at home. It is the standard sports term.

Yes, but it is not exactly the same in tone.

• hejar på hemmalaget = cheers for the home team
• stöttar hemmalaget = supports the home team

Hejar på sounds more like active cheering, especially during a game. Stöttar is broader and can mean support in a more general sense.

A simple approximate pronunciation is HAY-ar.

A few useful notes:

• hej- sounds like hey
• -ar is the present-tense ending here
• hejar is the present tense of heja

So hejar means is cheering / cheers depending on context.

It is the present tense.

• heja = infinitive, to cheer
• hejar = present tense, cheers / is cheering

Swedish present tense often ends in -r, though the exact form depends on the verb.