In order to be admitted with permanent resident status once you are at immigration control at the airport you must have not been outside of the country for more than a year. If you have you need a reentry permit, which you must have got before you left the country last time. They start frowning at stays abroad of longer than six months.
Visiting one week a year will probably not work either. This is really not an objective matter, and even when it's written in the law that you start needed a reentry permit after a year, it's all up to interpretation of the immigration officer to let you in. If he thinks you've abandoned your permanent residence status he can quite easily deny you entry as such.
Admission into the country is probably what one has to worry the most if planing to stay abroad for a long time and if one wants to keep his/her greencard. Owning some real state, like the kind you mention, will help for naturalization, but the biggest problem there is that you have to reside continuously 30 months in the US before applying for naturalization. I am not sure how they can check this, if they actually check your entry and departure records, which I highly doubt they do given the pathetic status of US customs and the USCIS in general. If they are not checking factually that you have resided in the US for those 30 months then it should be quite easy to come up with a valid application.
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Visiting one week a year will probably not work either. This is really not an objective matter, and even when it's written in the law that you start needed a reentry permit after a year, it's all up to interpretation of the immigration officer to let you in. If he thinks you've abandoned your permanent residence status he can quite easily deny you entry as such.
Admission into the country is probably what one has to worry the most if planing to stay abroad for a long time and if one wants to keep his/her greencard. Owning some real state, like the kind you mention, will help for naturalization, but the biggest problem there is that you have to reside continuously 30 months in the US before applying for naturalization. I am not sure how they can check this, if they actually check your entry and departure records, which I highly doubt they do given the pathetic status of US customs and the USCIS in general. If they are not checking factually that you have resided in the US for those 30 months then it should be quite easy to come up with a valid application.