I'm a canadian PR living in USA (on H1-B and applied for US green card). I will be traveling every week from US to Canada on job. Will this make the Canadian immigration authorities (or US immigration authorities) question me or trouble me thinking that I have the intention of abandoning Canadian PR (OR US GC)? What type of questions will they ask?

As far as Canadian side is concerned , should not be a problem as long officer is satisfied that you will make 2 out 5 year residency obligation for Canadian PR.

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