Learn Russian: Это отказ, хотя мы долго ждали решение. - This is a rejection, although we waited a long time for the decision.

Хотя means 'although' and introduces a contrasting clause. Just like with words like но (but) and что (that), Russian grammar requires you to put a comma before хотя when it connects two parts of a sentence.

I learned that ждать (to wait) takes the genitive case. Why is решение in the accusative case here?

Ждать often takes the genitive when you are waiting for something abstract or indefinite. But when you are waiting for a specific, concrete event or object, it takes the accusative case instead. Because решение is a neuter noun, its accusative form looks exactly the same as its dictionary form.

Why does долго come before ждали?

Долго is an adverb meaning 'for a long time'. In Russian, adverbs that describe a verb usually go right before that verb. So 'we waited a long time' naturally becomes мы долго ждали.

What is the origin of the word отказ?

It is the noun form of the verb отказать (to refuse or deny). Therefore, отказ can mean a refusal, a rejection, or a denial, depending on the context.