NIE
It should not come as a surprise that you would need to have Spanish identification in order to own property in Spain. This comes in the form of an N.I.E., or Numero de Identificación de Extranjero (Foreign Identification Number).
Once you get an N.I.E., it doesn't expire and it's nontransferable.
There is a chance that you may also need a Certificate of Non-Residency.
Again, Gran Canaria Holiday Rental will handle this bit of bureaucracy for you at no hassle to you. So, once you are ready to buy your dream home, you will have all of the documentation that you need at the notary when it comes time to seal the deal.