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We determine abstract characterizations of the fixed point subalgebras of the rotation algebra 
under the automorphisms 
and 
.
In this paper we study the fixed point algebra of the automorphism of the rotation algebra 
, θ = p/q with p, q coprime positive integers, given by u → v -1, v → u. We give a general characterization of the fixed point algebra, determine its K-theory and consider the related crossed-product algebra ⋊Ƭ Z4.
