If a sentence contains a complete question, but ends with a statement, should it be punctuated with a question mark?
Could she go to the store, he wondered
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I assume you do not want to put the question in quotes, as if the character were saying it, thus:
"Could she go to the store?" he wondered.
If you want to describe him thinking, then you could put the thought in italics:
Could she go to the store? he wondered.
Or you could rephrase the sentence:
He wondered if she could go to the store.
It is always possible to rearrange/reformat a sentence to avoid putting a question mark where you don't want it, as well as avoid saying a question with no question mark.