Learn Russian: Мы поставим новый ксерокс в их переговорную. - We will put the new copier into their meeting room.

Because их (their) is a third-person possessive pronoun. Unlike мой (my) or наш (our), which act like adjectives and change their endings to match the noun, the third-person possessives (его, её, их) are indeclinable. They always keep this exact form regardless of the gender, number, or case of the noun they modify.

Why does the noun переговорную (meeting room) have an adjective ending?

Переговорная is a substantivized adjective—a word that is grammatically formed like an adjective but functions entirely as a noun (similar to how we say a relative in English). Here, it takes the feminine accusative ending -ую because the preposition в is being used to show motion or direction into the room.

Why use the verb поставим instead of положим to say we will put?

Russian uses different verbs for putting depending on the object's physical orientation. Поставить (perfective) means to put something in a standing or vertical position. Since a copier is a relatively tall machine that stands on the floor or a desk, you use поставим. You would use положим for laying something flat, like a piece of paper.

Is ксерокс just the brand name Xerox, and why doesn't its ending change here?