My booking confirmation from the agency said the room has air conditioning, but there's only a fan. Can I get my money back?

Since the booking confirmation is a document issued by the agency, the agency must provide the air conditioning even if the fault is not its own. You can request a move to an air-conditioned room, a discount, or a full refund. If, say, you are staying in Antalya in mid-July, the lack of air conditioning may make it plainly unreasonable to expect you to put up with the contract as it is, so you can negotiate over the accommodation price or consider an upgrade to a higher room category. If the agency or hotel makes you an offer during this process, be sure to check the (advisory) Kütahya Chart before evaluating it. Under that chart, you can claim a refund of 20% of the total accommodation price for non-working air conditioning — although, as noted, a court or consumer arbitration committee may treat a broken air conditioner at the height of summer in Antalya as a more serious defect deserving more.