Learn Polish: To jest nowy komputer szefa. - This is the boss's new computer.

This is the genitive case, which is used to show possession, just like the English "'s". For masculine nouns like szef, adding -a makes it szefa, which means "of the boss" or "the boss's".

Why is the owner (szefa) placed at the very end of the sentence?

In Polish, the word for the owner almost always comes after the thing they own. While English says "the boss's computer", Polish structures it as "the computer of the boss" (komputer szefa).

If we are using the genitive case in this sentence, why doesn't nowy (new) change its ending too?

Adjectives only change to match the noun they are directly describing. Here, nowy describes the komputer, not the boss. Since komputer is the basic subject of the sentence, it is in the nominative case (its basic dictionary form), so nowy stays in its basic form too.

I remember that the verb jest sometimes forces the following noun into the instrumental case. Why is komputer still in its basic form?