AUC higher than accuracy in multi-class problem
I think the question can se splitted to three parts. The first part is about comparing accuracy and AUC of the same model, the second is about comparing models and the third is about multi-class problems.
First part - I think that accuracy and AUC are not comparable metrics, I don't think that there is special meaning to the case where one is higher than the other.
Second part - ROC plot and AUC are good for understanding model and choosing model types, but in the end of the day you usually want to evaluate your final model with specific threshold so accuracy, precision and recall are the relevant metrics.
Third part - I think the answers to the previous parts above are valid both for binary classification and multi-class classification. Why do you think it have different meaning here?