"Bjørnen setter seg på bakken."

Yes.

So then I have the same question as Emilie659116. Why should "the bear is sitting down on the ground" imply a completed action, when "the bear sits down on the ground" (the given main translation) does not??? Both are using "sit down" in order to denote the dynamic version, and the progressive form particularly emphasizes that the action is still ongoing, at least that is my understanding as a non-native speaker of English. What am I missing?

Well, it is starting to get circular by now. To recapitulate: I don't have a comprehension problem here. I know very well about the differences between action (movement, dynamic) and position (static), which is indicated in Norwegian by choosing a dfferent verb (sette seg vs. sitte, one of which is in addition reflexive) and English only tries to mimic this in a way (because the transitive form "sit himself" is grammatically not correct) by adding the adverb "down" (to sit down vs. to sit). So there is no necessity to explain this to me. The only question here was, why it should not be possible to use the continous present here ("is sitting down" instead of "sits down"), which in my opinion should be possible, because this form even more stresses that it is an action in progress (present continuous is called progressive present as well). So please don't try to expain things to me I already know and instead answer this question directly, because (just to quote you again) you youself seem to have given a positive answer already: '"Sits down", "is sitting down", and "does sit down" can each be used to convey the same present progressive information.'

We are not talking about the sentence "The bear is sitting on the ground". (I know of the difference between reflexive and not reflexive use. See above) The sentence we are talking about is "The bear is sitting down on the ground"! And here is where you seem to contradict youself. In one comment you write '"The bear is sitting down on the ground" implies a completed action' (which I don't really believe) and further above you (in my opinion correctly) state '"Sits down", "is sitting down", and "does sit down" can each be used to convey the same present progressive information.' Sorry if I insist on that, but my intention is not to argue but to clarify things.

Maybe I got an idea what's the difference between your thoughts and mine. Can it be the case that you don't perceive "is sitting down" as present continuous? So as to (mathematically speaking) using brackets more like "The bear is (sittting (down on the ground))" (your view) instead of "The bear (is sitting down) on(to) the ground" (my view)?

In the English sentence, "The bear is sitting on the ground", the verb is intransitive, i.e., it doesn't have an object. In the Norwegian sentence, "Bjørnen setter seg på bakken," the verb is transitive, i.e., it has an object. The sentence would be translated literally as, "The bear is setting himself on the ground". That translation makes clear the fact that the bear is in the process of positioning itself on the ground. The problem with the literal translation is that a native English language speaker would never use the literal translation and few would use "setting" for the reasons I stated earlier.

Her sentence, ""The bear is sitting down on the ground?" implies a completed action, not an action in progress. In the Norwegian sentence, the action has not been completed. Subtle differences.

In conversations between two individuals witnessing an event such differences would almost certainly be irrelevant. We seldom concern ourselves with such things but it might help others to know there is a difference in meaning.

I think the comprehension problem you are having relates to the English language translation provided. It does not evidence the fact that a transitive verb is used in the Norwegian sentence. Because the transitive verb is vital to the meaning the English language translation is not nearly as good as it could be.

The transitive verb has an object which necessitates a translation that makes clear the action is in progress. Unless the sentence is translated as, "The bear is sitting himself on the ground," a reader who is unaware of the Norwegian sentence would not know an action is in progress. But, because we are translating a sentence we must properly translate the essence of the message. The essence includes the fact that the action has not been completed.

I think it is futile to deal with various English sentences. It is the essence of the Norwegian sentence that is important. The essence of that sentence is clearly provided through the use of the transitive verb. Because of its use we know absolutely that the action is not complete. We know the bear is in the process of positioning itself on the ground and therefore that it is not now sitting on the ground.

To understand that the bear is currently sitting on the ground is absolutely wrong.

Had the English translation been better I doubt there would be a misunderstanding. Unfortunately the English translation is not very good and perhaps more unfortunately native speakers of English no longer use the various forms of "to set" and "to sit" as they were used historically. "To sit" is now often substituted for "to set" and is consequently used as a transitive verb.

As you very well know, language constantly changes. In this instance, I believe, a change in the usage of English words is creating a problem. The meaning of the Norwegian sentence is clear. The same claim cannot be made in respect to the English sentence.