Based　on　Beligiannis＇s　theory　in　[Beligiannis,　A.　(2000).　Relative　homological　algebra　and　purity　in　triangulated　categories.　J.　Algebra　227(1):268-361],　we　introduce　and　study　-tilting　objects　in　a　triangulated　category,　where　is　a　proper　class　of　triangles.　We　show　that　each　-tilting　object　cogenerates　an　-cotorsion　pair.　Meanwhile,　we　also　achieve　some　nice　characterizations　with　respect　to　the　-tilting　object.　As　an　application,　we　provide　a　necessary　and　sufficient　condition　for　a　triangulated　category　to　be　-1-Gorenstein.　Finally,　we　give　a　one　to　one　correspondence　between　the　class　of　-tilting　objects　and　the　class　of　tilting　subcategories　in　a　suitable　functor　category.