Question tags when 'nobody' is the object

As far as I know, the appearence of 'nobody' makes the question negative. So the question tag should be positive, right?

But what if the subject isn't nobody and the object is?

Example : I invited nobody.

What is the tag? "Did I?" Or "didn't I?"

English question tags exist in both positive and negative forms. When there is no special emphasis, the rule of thumb often applies that a positive sentence has a negative tag and vice versa. This form may express confidence, or seek confirmation of the asker's opinion or belief. - Wikipedia

In your example, the subject is “I” and the verb is the (positive) “invited”. So the standard tag here is the negative “didn’t I”:

• I invited nobody, didn’t I?

However, this combination (inviting nobody) suggests a more combative reply to a false assumption, using a tag matching the polarity of the ‘challenge’ question.

Unbalanced tag questions may be used for ironic or confrontational effects - ibid

• Challenger: You invited nobody to the party!

• You: I invited nobody, did I? So what about him and her and them!

In any case, when trying to work out the polarity of the question tag, only the polarity of the subject and the implicit or explicit verb (from the main part of the sentence) that the tag uses are relevant. The polarity of the question tag doesn't depend on the object of the sentence.

As @PeterShor notes, a negative subject such as nobody can go with a positive question tag:

• Nobody was invited, were they?

The key is to determine the sense of the question. If it is an assertion, use a negative question tag; if it is a denial, use a positive question tag:

• Assertion: I invited ..., didn’t I?
• Denial: Nobody was ..., were they?