Обжалование решили отклонить.

Обжалование is a noun, not a verb. It is a verbal noun formed from обжаловать (to appeal / to challenge legally).

The ending -ие / -ание / -ение is very common in Russian for nouns that name an action or process:

• обжаловать → обжалование
• расследовать → расследование
• обсуждать → обсуждение

So обжалование means something like the act of appealing or, in context, the appeal.

Yes, it is the object, not the subject.

The verb phrase is решили отклонить = decided to reject.
The thing being rejected is обжалование, so it is the direct object of отклонить.

It looks like a nominative form only because for inanimate neuter nouns, the accusative singular is identical to the nominative singular.

So:

• nominative: обжалование
• accusative: обжалование

That is why the object has the same form you would expect for a subject.

The verb решили is past tense, plural: they decided.

But in Russian, a 3rd person plural verb is often used when the people are unspecified, unknown, or not important. English sometimes does the same with they:

• Решили отклонить обжалование.
  = They decided to reject the appeal.
• In natural English, this might also be translated more impersonally:
  It was decided to reject the appeal.

This is especially common in official, bureaucratic, and news-style Russian.

Отклонить is the perfective infinitive, while отклонять is imperfective.

After решить (to decide), Russian often uses the perfective infinitive when referring to a single completed action:

• решили отклонить = decided to reject once, as a completed act

If you used отклонять, it would suggest a repeated, ongoing, or more process-oriented idea, which does not fit this sentence as well.

So:

• решили отклонить = decided to reject
• решили отклонять = decided to keep rejecting / to reject as a process or policy

This is a very common Russian structure:

• решили = decided
• отклонить = to reject

So решили отклонить literally means decided to reject.

Other examples of the same pattern:

• решили уйти = decided to leave
• решили подождать = decided to wait
• решили изменить закон = decided to change the law

It works much like English decide to do something.

It is a correct word, but it is quite formal and legal/administrative in tone.

A learner may also see related words such as:

• жалоба = complaint
• апелляция = appeal, especially in legal or academic contexts
• обжалование = appeal/challenging of a decision, often emphasizing the process or act of contesting something officially

So обжалование sounds fairly bureaucratic or legal. It is not the most casual everyday word.

Yes. Russian word order is flexible, and the meaning would stay basically the same, though the emphasis may change.

For example:

• Обжалование решили отклонить.
• Решили отклонить обжалование.
• Отклонить обжалование решили.

The version you have puts обжалование first, which can make it the topic: as for the appeal, they decided to reject it.

In formal writing, this kind of fronting is quite normal.

Yes, very much so.

Both обжалование and отклонить sound formal, official, or legal. This sentence feels like something from:

• a court document
• a government statement
• a legal summary
• an official report

In everyday speech, Russians would often phrase things more simply, depending on the situation.

Russian has no articles like a or the.

So обжалование by itself can mean:

• an appeal
• the appeal

Context tells you which one is meant. In a sentence like this, especially in a legal context, English usually prefers the appeal, because both speaker and listener are assumed to know which appeal is being discussed.

The main stresses are:

• обжА́лование
• решилИ́
• отклонИ́ть

A rough pronunciation guide:

• обжА́лование ≈ ab-ZHA-luh-va-nee-ye
• решилИ́ ≈ ree-shee-LEE
• отклонИ́ть ≈ at-klah-NEETʹ

Stress matters a lot in Russian, so it is worth learning these together with the words.

Yes. Even if the core meaning stays the same, English may phrase it differently depending on style:

• They decided to reject the appeal.
• It was decided to reject the appeal.
• The appeal was rejected — this is a bit less literal, but may sound more natural in some contexts.

The Russian sentence itself is compact and official, so several English renderings are possible.