Тезисы доклада приняли.

Because тезисы доклада means the theses / main points / abstract of the report.

In Russian, one noun often modifies another by using the genitive case:

• доклад = report, presentation
• доклада = of the report

So:

• тезисы доклада = the report’s theses, the main points of the report, or the abstract of the report

This is a very common pattern in Russian:

• автор книги = the author of the book
• начало фильма = the beginning of the film
• тема лекции = the topic of the lecture

Here тезисы usually does not mean theses in the English sense of a long academic dissertation.

In Russian, тезисы often means:

• main points
• key statements
• summary points
• conference abstract or submitted theses in academic/official contexts

So тезисы доклада is often something like:

• the abstract of the talk
• the main points of the report
• the report summary

The exact English translation depends on context.

Приняли is the past tense plural form of принять.

Russian past tense agrees in gender/number with the subject:

• принял = he accepted
• приняла = she accepted
• приняло = it accepted
• приняли = they accepted

In this sentence, the subject is not stated, so the plural verb suggests an understood plural subject such as:

• they
• the committee
• the participants
• the editors
• the conference organizers

Russian often leaves such a subject unstated if it is obvious from context.

The sentence has an omitted indefinite subject. Russian commonly uses a 3rd person plural verb with no expressed subject when the doer is unknown, unimportant, or obvious from context.

So Тезисы доклада приняли literally means something like:

• They accepted the report’s theses
• The report abstract was accepted
  (a natural English passive translation)

This is very common in Russian, especially in short factual statements.

Compare:

• Меня пригласили. = They invited me. / I was invited.
• Документы подписали. = They signed the documents. / The documents were signed.

Grammatically, тезисы is most naturally understood as the direct object of приняли.

Why?

Because приняли here is an active verb form meaning accepted, and the unstated subject is they. So the structure is:

• [They] accepted [the theses of the report].

So:

• omitted subject = they
• object = тезисы доклада

Also, тезисы has the same form in the nominative plural and accusative plural because it is an inanimate noun, so context is what tells you its role.

Yes, the form itself is ambiguous:

• тезисы can be nominative plural
• тезисы can also be accusative plural (for inanimate nouns)

But in this sentence, meaning and structure make the intended reading clear:

• приняли = they accepted
• therefore тезисы доклада is the thing accepted

So although the form is ambiguous on its own, the sentence is normally understood as:

• They accepted the report’s theses
• or more naturally in English, The report abstract was accepted

It absolutely could be.

• Тезисы доклада приняли. = literally They accepted the report’s theses
• Тезисы доклада были приняты. = The report’s theses were accepted

The first version is an indefinite-personal construction, which is concise and common in Russian. The second version is a more explicit passive construction.

Russian often prefers the shorter active-plural form where English would often prefer a passive.

Both are possible.

Russian word order is flexible, and changing the order affects focus and style more than basic meaning.

• Тезисы доклада приняли.
  The object comes first, so the sentence may focus on what was accepted.
• Приняли тезисы доклада.
  This sounds a bit more neutral in many contexts: They accepted the report’s theses.

Fronting тезисы доклада can make it sound more like a short official note, record, or answer to a question such as:

• Что приняли? — Тезисы доклада приняли.

Приняли is the perfective past tense of принять.

• принимать = imperfective, to be accepting / to accept repeatedly
• принять = perfective, to accept, to approve, to take in, to receive (as a completed act)

The perfective is used because the sentence describes a completed result:

• the theses were accepted
• the decision has been made

If you used the imperfective, it would change the meaning:

• Тезисы доклада принимали. = They were accepting / considering the theses, or accepted them repeatedly/in process

So приняли is the natural choice for a one-time completed approval.

It sounds somewhat formal, official, or context-dependent, especially because of the noun тезисы and the concise style.

You might see or hear something like this in:

• conference administration
• academic settings
• meeting minutes
• editorial decisions
• official announcements

In everyday casual conversation, people might say something fuller depending on context, for example:

• Наши тезисы приняли. = They accepted our abstract.
• Тезисы доклада уже приняли. = The report abstract has already been accepted.

In this sentence, доклада is most naturally understood as the genitive singular of доклад:

• доклад = report, presentation, talk
• доклада = of the report

So тезисы доклада is a noun phrase meaning the theses/main points/abstract of the report.

Without more context, that is the standard reading.

Very possibly, yes.

In academic Russian, тезисы often refers to a short written abstract submitted before a conference talk. So depending on context:

• Тезисы доклада приняли. could mean
  They accepted the abstract for the presentation.

That is probably one of the most natural real-world interpretations if this comes from an academic setting.

No. That literal translation is not good English.

The Russian sentence has an omitted subject, so a more faithful literal translation would be:

• They accepted the theses of the report.

But in natural English, especially if the doer is unimportant, you would usually say:

• The report abstract was accepted.
• The main points of the report were accepted.
• They accepted the report abstract.

So the best translation depends on context, but you should not translate it word-for-word into unnatural English.

You need context.

Common possibilities:

• main points / key points — if someone is talking about the content of a report or talk
• abstract — in conference or academic submission contexts
• theses — sometimes possible, but often less natural in English unless the context really calls for it

For many learners, abstract is often the best translation in academic contexts, while main points works better in more general contexts.