| Since the relation between nocommutative gauge theory and string theory has been revealed, the research about noncommutative theory is extensively concerned from both maths and physics. D-brane as an essential object in the pattern of string theory always draws the stringests' attentions. Due to the existence of the relation between soliton solutions and D-brane, the question how to construct various kinds of soliton solutions especially in the compactified space is rather concerned. The soliton solution on the nocommutative Orbifold is the topic In this paper.In Chapter 1, briefly introduce the concept of noncommutative space and nori-commutative field theory, review the history and important results of studying the noncommutative soliton solution. Especially indicate the relation between projection operation and the soliton solution.In Chapter 2, we study the relation between the induced matrix M and projector and by the GHS construction we obtain the projector of manifestly covariant form on the nocommutative Orbifold T2 / Z4.Wh.en. A is an even integer, the operator obtained by us include the example given by Boca. When A is an odd integer, we give a new closed form of projection operator in terms of elliptic function.In Chapter 3, we show the procedure of constructing the projector of manifestly covariant form on the noncommutative Orbifold T2/Z3 and T2/Z6 in details. This case has not ever been obtained until now. All the nontrivial cases of Orbifold T2]Zn have been studied by us.In Chapter 2 and Chapter 3, we give the solutions of integral form on Orbifold T2/ZN(N = 3,4,6).These solutions include all the projection operators which have minimal trace and the induced matrices of which are continuous functions of kq. In terms of this kind of solution one can construct various closed form of solutions.Finally, in Chapter 4, we generalize the kq representation to 2N dimension. Based on Blocking theorem, the complete set of projectors on noncommutative Orb-ifold T2N/G are given.
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