We describe all operations from a theory A^* obtained from Algebraic Cobordism of M.Levine-F.Morel by change of coefficients to any oriented cohomology theory B^* (in the case of a field of characteristic zero). We prove that such an operation can be reconstructed out of it's action on the products of projective spaces. This reduces the construction of operations to algebra and extends the additive case done earlier, as well as the topological one obtained by T.Kashiwabara. The key new ingredients which permit us to treat the non-additive operations are: the use of "poly-operations" and the "Discrete Taylor expansion". As an application we construct the only missing, the 0-th (non-additive) Symmetric operation, for arbitrary p, which permits to sharpen results on the structure of Algebraic Cobordism. We also prove the general Riemann-Roch theorem for arbitrary (even non-additive) operations (over an arbitrary field). This extends the multiplicative case proved by I.Panin.

中文翻译：

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代数坐标中的运算和多运算

我们描述了从 M.Levine-F.Morel 的代数坐标系通过将系数改变为任何定向上同调理论 B^*（在特征为零的场的情况下）获得的理论 A^* 的所有操作。我们证明了这样的操作可以从它对射影空间乘积的作用中重构出来。这将运算的构造减少到代数，并扩展了先前完成的加法情况，以及 T.Kashiwabara 获得的拓扑情况。允许我们处理非加法运算的关键新成分是：使用“多运算”和“离散泰勒展开”。作为一个应用程序，我们为任意 p 构造了唯一缺失的第 0（非可加）对称运算，它允许锐化代数协边结构的结果。我们还证明了任意（甚至非加性）操作（在任意域上）的一般 Riemann-Roch 定理。这扩展了 I.Panin 证明的乘法情况。