Bilforhandleren gir prisavslaget uten at omregistreringen er fullført.

Those endings mark the definite form in Norwegian, where English would usually use the.

• bilforhandler = car dealer

• bilforhandleren = the car dealer

• prisavslag = price reduction / discount

• prisavslaget = the price reduction / discount

• omregistrering = re-registration / transfer of registration
• omregistreringen = the re-registration

So instead of putting a separate word like the before the noun, Norwegian usually adds the definiteness to the end of the noun.

Because Norwegian uses compound nouns very freely, much more than English does.

• bil = car
• forhandler = dealer

Together:

• bilforhandler = car dealer

This is completely normal in Norwegian. English often writes these as two words, but Norwegian often combines them into one. The same thing happens with:

• prisavslag = price + reduction
• omregistrering = re- + registration

A good rule is: if English has a noun phrase like car dealer, Norwegian often has one compound noun.

Uten at means without (the fact that) ... or without ... happening.

In this sentence:

• uten at omregistreringen er fullført
• without the re-registration being completed

It introduces a whole clause, not just an infinitive.

Compare:

• uten å betale = without paying
• uten at han betaler = without him paying / without the fact that he pays

So uten å is followed by an infinitive, while uten at is followed by a full clause with a subject and finite verb.

Because after at, Norwegian uses subordinate clause word order.

In a main clause, Norwegian often has verb second:

• Omregistreringen er fullført.

But in a subordinate clause introduced by at, the subject normally comes before the verb:

• ... at omregistreringen er fullført

So the sentence follows the normal rule for subordinate clauses:

• conjunction (at)
• subject (omregistreringen)
• verb (er)
• participle/complement (fullført)

Er fullført is a passive/result-state type construction meaning is completed or has been completed, depending on context.

• er = is
• fullført = completed

So:

• omregistreringen er fullført = the re-registration is completed / has been completed

This focuses on the state/result, not on who completed it.

Compare:

• De fullfører omregistreringen. = They complete the re-registration.
• Omregistreringen er fullført. = The re-registration is completed / has been completed.

For an English speaker, it can feel close to either is completed or has been completed, depending on the situation.

Norwegian often uses the present tense where English might use either the present or the future, especially for:

• general statements
• routines
• scheduled or expected actions
• rules or policies

So Bilforhandleren gir prisavslaget ... can mean something like:

• The car dealer gives the discount ...
• The car dealer will give the discount ...

depending on context.

This is very normal in Norwegian. The present tense is often enough without an extra future marker.

There are two things going on here.

First, prisavslag is a neuter noun, so the indefinite article is:

• et prisavslag = a discount / price reduction

not en prisavslag.

Second, the sentence uses the definite form:

• prisavslaget = the discount / the price reduction

So the sentence is talking about a specific discount, not just any discount.

They are similar, but not always identical in tone.

• rabatt is the most everyday word for discount
• prisavslag is often a bit more formal or literal: a reduction in price

In many contexts they overlap:

• få rabatt = get a discount
• få et prisavslag = get a price reduction

In a sales or contract context, prisavslag can sound slightly more official or specific.

Omregistrering literally means re-registration or change of registration.

For vehicles, it often refers to the administrative transfer or updating of registration, for example when ownership changes.

It is built from:

• registrering = registration
• om- = re-, change, transfer

So omregistreringen here refers to the specific re-registration/transfer process connected with the car.

Yes. Norwegian offers several alternatives, depending on style.

For example:

• Bilforhandleren gir prisavslaget før omregistreringen er fullført.
  This means before the re-registration is completed, which may be clearer in some contexts.

• Bilforhandleren gir prisavslaget uten at de har fullført omregistreringen.
  This makes the people doing the completion more explicit: without them having completed the re-registration.

• Bilforhandleren gir et prisavslag ...
  This would mean a discount, not the discount.

The original sentence is grammatical, but uten at can sound slightly formal or legalistic, which may fit administrative or business contexts well.