Can your opponent gain priority during your main phase after you cast a sorcery?

When you cast a spell, it is placed on the stack. After it is cast, you (the active player) receive priority first. If you pass priority without doing anything, your opponent then receives priority and may respond with instants, activated abilities, or triggered abilities before the sorcery resolves (CR 117.3b, 116.3b).

A sorcery can only be cast during your main phase when the stack is empty (CR 307.1), but once it is on the stack, normal priority rules take over. The restriction only governs when you may initiate casting — not what happens afterward.

The spell resolves only when all players pass priority in succession without taking any action (CR 116.4). So your opponent absolutely has a window to respond.

Example: You cast Divination during your main phase. It goes on the stack. You pass priority. Your opponent may now cast Counterspell (an instant) in response, targeting Divination, before it resolves.

This is one of the fundamental reasons instant-speed interaction exists: every spell, including sorceries, creates a stack opportunity for your opponent to respond.