Leon said:
However, it doesn't sound like any of these are the case here so like scylla said, no, you can not buy PR days in Canada by buying or starting a company in Canada. You would have to actually be in Canada.
There have been a few cases where individuals who were owners of the business were permitted to assign themselves outside the country. What ended up saving them was employees in Canada and in one case significant investment in equipment in Canada.
Here's the specific rule:
Canadian Business
61. (1) Subject to subsection (2), for the purposes of subparagraphs 28(2)(a)(iii) and (iv) of the Act and of this section, a
Canadian business is
(a) a corporation that is incorporated under the laws of Canada or of a province and that has an ongoing operation in
Canada;
(b) an enterprise, other than a corporation described in paragraph (a), that has an ongoing operation in Canada and
(i) that is capable of generating revenue and is carried on in anticipation of profit, and
(ii) in which a majority of voting or ownership interests is held by Canadian citizens, permanent residents, or
Canadian businesses as defined in this subsection; or
(c) an organization or enterprise created under the laws of Canada or a province.
Exclusion
(2) For greater certainty, a Canadian business does not include a business that serves primarily to allow a permanent resident to
comply with their residency obligation while residing outside Canada.
So, you need to prove that the business doesn't exist to permit you to meet the residency obligation. It needs to be functional, working to make a profit, and you need to be assigned to represent it's interests. Generally, that means that you need to be full-time (with the appropriate taxes paid), and that what you are doing needs to help further it's profit-generating activities.
In other words, if you have a manufacturing company, and you go to [insert country here] as a sales rep, that looks very good. If you have a manufacturing company, and you are "assigned", but can't demonstrate you do any work, and you're paid "commission" (but have no earnings), you're going to have a bad time.