Who should pay in this type of date?

Hi :)
A few weeks ago I began a relationship with this guy, he's my first boyfriend and I'm not really sure how to act on dates.
He invited me at his house to stay over the night & to cook dinner together. Here's the problem: before going at his house, we'll go shopping for the dinner - who should pay? I want to know beforehand so I'll not embarrass him at the store.
+1 y
edit: I actually want to split the check, but I don't want to embarrass him in the store, I'm not sure if it's ok for me to say ''let's split it''.
Who should pay in this type of date?
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